Thirty-five years ago, Salman Rushdie published an essay titled “Imaginary Homelands,” in The London Review of Books. “It may be that when the Indian writer who writes from outside India tries to reflect that world, he is obliged to deal in broken mirrors,” Rushdie wrote. But “the broken mirror may actually be as valuable as the one which is supposedly unflawed.” Rushdie was describing his difficulties in remembering and conjuring up his homeland after moving to London and writing his magnum opus, “Midnight’s Children.” As an exile, he struggled to see, as in a shattered mirror, his former country, yet the process taught him something integral to so much immigrant fiction: that there is no single version, no sole reflection, of any place.

Pajtim Statovci, whose first novel, “My Cat Yugoslavia,” has just been published in English, was born in Kosovo; his family fled to Finland in 1992, when he was two years old. War had broken out the year before in what was then Yugoslavia, after Croatia and Slovenia declared independence—the Yugoslav Wars, which pitted several ethnic groups against one another, lasted for a decade. “When I told people where I come from, instead of interest, I many times received pity,” Statovci told me recently. He felt inextricably connected to Kosovo but also alienated from a place he’d only faintly known. And as a gay man now growing up Muslim in a predominantly Christian country, he felt a profound sense of dislocation.

“My Cat Yugoslavia” draws on this compounded experience of exile to tell two parallel stories; it reads as a life reflected by flawed and foggy mirrors. In the nineteen-eighties, a young Muslim girl in Kosovo, Emine, is married off to Bajram, a man whom she thinks she loves but who quickly proves abusive. Like Statovci’s parents, Emine and Bajram flee their country for Finland, and the novel’s second story line is narrated by their lonely son, Bekim, who grows up there. Finland provides safety from the war, but the family quickly encounters new difficulties, as anti-immigrant and anti-Muslim sentiment prove disquietingly commonplace in their new home. Bekim is made to feel ashamed of his roots in Kosovo, which is constantly depicted in the news as a horrific place broken by war. He starts to use false names, like Michael and John, simply to “avoid the next question, which is, ‘Where are you from?’ ” “It’s one thing to tell someone you are Swedish, German, or English,” Bekim says, “and quite another thing to say you are Turkish or Iranian. It’s only very rarely that someone’s home country is of no significance at all.”

When Bekim begins sleeping with men, those he meets are often living double lives, going home to wives and sneaking in the shadows for sexual assignations. Eventually, Bekim leaves his father’s home and lives a largely isolated existence, punctuated by his purchase of a boa constrictor. The pet serpent becomes a peculiar character in its own right, its reptilian coolness and shedding of skin reflecting Bekim’s progressive loss of his own warmth. The book’s most notable animal, however, is the one in the title: an anthropomorphic talking cat named Yugoslavia, whom Bekim meets at a gay club. The cat quickly charms Bekim, despite sharing so many of the hatreds that torment him: the cat is anti-gay, anti-immigrant, and as selfish and abusive as Bekim’s father. Even so—and much as his mother did, for years, with his father—Bekim caters to Yugoslavia, bringing the cat home and attending to its every need.

This unusual relationship, Statovci told me, may represent, for Bekim, “a different kind of love” from the others he has known, “stronger and more powerful, because it has crossed borders and walls. Maybe he thinks that if he can get someone like that to give him love and acceptance, he will be O.K.,” Statovci added. “Maybe he needs to feel that it is possible for people who think in a similar way the cat thinks to see him as more than a refugee or as a gay guy—to fall in love with him.”

Statovci has long been haunted, he told me, by George Orwell’s “Animal Farm,” particularly the famous line “All animals are equal, but some animals are more equal than others,” which Statovci called “a beautiful analogy of the world we live in.” Yugoslavia the cat may also remind readers of Behemoth, the demonic feline in Mikhail Bulgakov’s “The Master and Margarita,” who mixes his devilry with charm, though Yugoslavia seems more devil than charmer. And midway through Statovci’s novel Yugoslavia becomes a regular house cat, which Bekim carries around. The novel never explains how or why a talking cat existed or what to make of his disorienting return to ordinariness. Had Bekim imagined Yugoslavia into existence out of desperation? Had something in him shattered, and Yugoslavia emerged? The feline’s shift may contain a cultural metaphor: in Finland, Statovci told me, “cats are domesticated, whereas in Kosovo they are seen as dirty.” But this only says so much. Perhaps, the novel seems to suggest, this is how a mind can break, folding in on itself, elaborate as an origami swan, until it is torn apart.

“My Cat Yugoslavia” is spry and warm at first, but it hardens, becoming emotionally icier, until Bekim and his mother reach parallel breaking points: Bekim returns to Kosovo to confront the phantoms of his past, and Emine leaves Bajram. This chilliness put me off at first; the novel’s coldness made me feel cold to it. But, as I kept reading, its mood and style began to make sense. The novel is a slowly shattering and re-forming reflection of the protagonists’ corresponding descents into wintry numbness, until, near the end, they begin to revive, and to love. When Emine receives a letter from the husband she has fled, she realizes it is addressed to someone “who no longer existed.” But the past does not disappear: even as Bekim walks, near the novel’s end, with the male lover his father would never have accepted, he cannot stop thinking of Bajram, cannot stop hearing the sharp words from his former life.

Perhaps this is the strange, phantasmal way the language of the past calls us from exile, the way the borderlands of an old identity may become less distinct the further we move away from it, without ever fully vanishing. We think we have left a world behind, only to realize we are still walking, somehow, along its edges. Like Statovci, I fled my country, not because of war but because of laws that criminalized being openly queer; as a trans woman, I fled, too, from the social appearance of a gender that did not define the contours of me, knowing, like Bekim, that something in me would shatter if I did not. I often feel that I’ve come to better understand both my former home and my former self by leaving each behind. And yet, when I look in my own mirror of the past, I still sometimes fear what I will see. “Writers in my position, exiles or emigrants or expatriates, are haunted by an urge to look back,” Rushdie wrote, “even at the risk of being mutated into pillars of salt.” Statovci’s surreal, arresting novel suggests that we must look anyway, and that love and identity have many reflections, many destinies, many languages. Sometimes, a broken mirror reflects something truer—as does the kind of love, drawn from the deepest sunken places, that tries to put it back together.