We compute the RO(C₂)-graded Bredon cohomology of certain families of real and complex C₂-equivariant Grassmannians.

This work is based on the author's doctoral dissertation. It is the product of many conversations with both his thesis advisor Dan Dugger and with Clover May, who each came to the rescue repeatedly. The author is grateful to both of them, as well as to Kelly Poland for spotting an error, and to the anonymous referee for numerous useful suggestions. This work was partially funded by University of Oregon and Gonzaga University.