Organized by Independent Curators International, ''The Gift: Generous Offerings, Threatening Hospitality'' at the Bronx Museum of the Arts has a fair amount of interesting work, most of it by contemporary figures familiar in New York (Vito Acconci, Louise Bourgeois, Kiki Smith), some by youngish Europeans little seen here (Claude Closky, Massimo Kaufmann, Matthieu Laurette). What's missing is focus, the sharpness of vision that produces a think-piece show that actually prompts some thinking.

True, the curatorial fine-tuning required might be misplaced in an exhibition intended, as this one is, primarily for touring, with inevitable adjustments and rearrangements in the show's format at every stop. But given the loaded political and social ideas brought up by its themes, you can't help but regret the absence of hard, synthesizing thinking here.

As it is, some two dozen individual pieces must make their different points more or less on their own, which is O.K. Many of them are up to the challenge. In a photographic diptych titled ''My Hands Are My Heart'' (1991), Gabriel Orozco taps into the notion of the gift as a self-sacrificial religious offering, with overtones of sensuality. In one of the two photos, he holds his hands together, at chest level. In the other, he opens them to reveal a lump of clay that his fingers have pressed into the form of a heart, which he holds out, as if for the asking.

The show also offers some real gifts, available to all. You can help yourself to pieces of candy from one of Felix Gonzalez-Torres's signature corner piles. And you can keep one of the striped cotton towels stacked in a pile outside Navin Rawanchaikul's video installation, which documents the myriad practical, daily uses this pretty but humble cloth has in his native Thailand.

Sometimes a gift comes with stipulations. If you take one of Lee Mingwei's origami sculptures made from dollar bills, you are expected to leave something -- anything you want -- in exchange. Similarly, you are welcome to use the folding metal chair that Jochen Gerz has left in the gallery, but only if you carry it out into the street and ask for handouts from passers-by while you sit, a provocative gesture given the shaky economic status of the surrounding Bronx neighborhood.

The show also presents examples of altruism in the form of self-serving versions of hospitality. In a piece by Cai Gui-Qiang, all the mass-produced terra-cotta figurines in a cardboard packing box depict a Chinese general who famously invited an enemy arrow assault to replenish his own ammunition. A video by the Japanese artist Yutaka Sone documents, in what seems like a sociable gesture, several birthday parties, yet Mr. Sone gave all of them to celebrate his own birthday, recruiting strangers as the guests.

Hospitality can take hostile forms: a doormat designed by Mona Hatoum spells out ''Welcome'' with thousands of upright needles. It can also be guilelessly utopian, as in a project titled ''The Gift'' by the Italian artist Mario Rizzi. Over the course of roughly a year, beginning in December 2000, Mr. Rizzi invited Palestinians and Jews he casually encountered in the streets of Tel Aviv, Jerusalem, Ramallah and other cities to take part in an anonymous, interethnic gift exchange, with all the participants contributing things they thought best symbolized their cultures.

To cap the year, he invited all the gift-givers to meet for a dinner and dance. In videos of the party seen at the museum, the food looks good (everybody made a dish); the music sounds great; and the conversation and dancing are lively. You'd never guess that these people were strangers before these festivities. But in a sense, they weren't. They were already bound together by mutual generosity.

Such sharing is the conceptual premise for a whole strain of contemporary American art. Artist groups like Law Office, based in Chicago, support projects conceived by other artists by providing service-oriented collaborations. Other groups, like Critical Art Ensemble, distribute countercultural political ideas, works and information through various media, including the Internet.

The Internet itself, ideally at least, is a mechanism for free exchange, its resources open to all. Among other things, it supplies rent-free gallery space for digital artists, including many who are using the space these days to produce and display work opposing a United States war against Iraq.

No interactive digital work is included in the Bronx show, which, despite its anti-materialist implications, is object-bound and conceptually restrained. At the same time, the show's very theme embodies a kind of karmic logic: in art, life and politics, what you cling to most tightly will sooner or later weigh you down, and what you give away will come back to you, for better and worse, in many forms.

''The Gift: Generous Offerings, Threatening Hospitality'' is at the Bronx Museum of the Arts, 1040 Grand Concourse, at 165th Street, Morrisania, (718) 681-6000, through March 2. It travels to the Mary and Leigh Block Museum of Art, Northwestern University, Evanston, Ill. (April 14 to June 15), and then to the Art Gallery of Hamilton, in Ontario. A panel discussion, ''Figures of Gift and Hospitality in Contemporary Art,'' will be held at the Bronx Museum on Wednesday at 7 p.m.