AMERICAN INNOVATIONS. By Rivka Galchen. FSG. 175 pages. $24.

In the stories of Rivka Galchen's first collection, "American Innovations," the ordinary is always open to assaults of the extraordinary. Really, anything can happen. These invasions of the fantastic dominate even the most banal plots.

Several of the stories explicitly pay homage to classically weird stories by men: Kafka's "Metamorphosis" (and Roth's knock-off, "The Breast"), Borges' "The Aleph," Gogol's "The Nose," and Thurber's "The Secret Life of Walter Mitty."

Galchen changes the gender of the estranged hero and fiddles with the details, often shifting the mood toward reverie.

How's this for a plot? A barber finds a nose in his morning loaf of bread. The nose, it turns out, has defected from the face of Kovalev, a college assessor who wakes to find his face smooth as a pancake. On his way to report the missing organ, Kovalev spies his nose wearing a gold-embroidered uniform, topped by a plumed hat, and jumping into a carriage. From the plumes on his hat, Kovalev realizes that the missing nose is now four grades above him in rank. So goes Gogol's hilarious "The Nose."

Galchen's version? In the story "Once an Empire," her unnamed narrator (they're all nameless) comes home to see her wooden ironing board stepping through the window of her studio apartment and onto the fire escape. Seeing it there, out of its context, "a great tenderness unearthed itself." Next goes a velvet recliner "with surprising nimbleness." Watching a little souvenir fork leave, the narrator feels "limbless." Like Britain, "once an empire," she's now just a small island, without her things.

Galchen's stories often tilt us toward an enlightenment that never comes and meaning that might be forever dammed up and incommunicable. The narrator's runaway objects tell a story of loss beyond repair and spiritual vacancy.

Again and again, some form of cosmic absurdity hints at a world that's unexplainably askew. The speaker of "American Innovations" wakes up one morning, like Kafka's Gregor Samsa, to find herself transformed. On her back is a lump, shaped like a modest, B-cup, "really textbook" breast. The doctor she visits asks a series of irregular diagnostic questions - Any regrets? Losses you haven't accepted? - before telling her, "Your body speaks a language. It's like a foreign language we all speak but have forgotten how to understand." In the end, the narrator "feels very feminine" and goes out to buy a mod dress.

Like the speaker of "American Innovations" - who doesn't know if she's sick or well, embellished or diminished - the narrator of Galchen's opening story, "The Lost Order," can't sort out what she wants or how to evaluate what she has. The first line of the story casts her life in a negative light: "I was at home, not making spaghetti." The lost order of the title is, literally, a lost take-out order. She answers an "Unavailable" call on her cell, accepts a take-out order for lemon chicken, and then endures call-backs when the order never arrives.

Declaring that a hungry man is no concern of hers, she repeats the excuse: He's Unavailable.

Meanwhile, another lost item may really signal the end of order. While she was away at a family funeral, the narrator's husband somehow lost his wedding ring. "We're not symbol people," she confides. As she moves through the day, the Walter Mitty-ish woman has, and rejects, multiple fantasies, so much so that her husband notices she's both there and gone at the same time. The story ends: "Maybe I'm the dreamer in the relationship after all. Maybe I'm the man."

It would be too pat to boil Galchen's stories down to treatises on the rank and privilege of gender, but there it is, hanging gigantically among the orders, this one gleefully, lost. In a Rivka Galchen story, there are many ways to live the wrong life.

Reviewer Catherine Holmes teaches English at the College of Charleston.