The Motivic Cohomology of Stiefel Varieties

Abstract

The main result of this paper is a computation of the motivic cohomology of varieties of n m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general linear group-scheme with a Tate suspension of a space which isA 1 -equivalent to projective n 1-space with a disjoint basepoint.