“It’s quite offensive,” he said. “It’s a form of conquest.”

Mr. Van Dunk, 54, a Brooklyn woodworker who is active in Native American issues, pointed out that, if such a transaction had taken place, the Lenape might have meant it as a good-will exchange for sharing the land, and not as transferring ownership, especially because the tribe did not believe anyone could own land or water.

The Lenape “tried to embrace and share,” Mr. Van Dunk said. “And in return, they got everything taken, even their lives.”

Now, of course, Manhattan — whose name comes from the Lenape tongue, meaning roughly “the land of many hills” — has been developed to the hilt into a center of global commerce.

“Manhattan is a capitalist rock; this is a quiet protest against that,” Mr. Bourgeois said of his gift. “I’m giving it back to whom the land was stolen from, and that’s really a joyful event.”

Mr. Bourgeois, a longtime Greenwich Village resident and an architectural historian, is a son of the sculptor Louise Bourgeois, who died in 2010. His large inheritance, from the proceeds of her art, has financed his activism, which is aimed at social and environmental causes.

Mr. Bourgeois said that he bought the building, 392 West Street, in 2006 for $2.2 million, and that it had probably appreciated in value to about $4 million. With three floors and less than 3,000 square feet, it is one of the last wood-frame buildings along the Hudson waterfront.