The Leray-Hirsch Theorem for oriented cohomology of flag varieties

Abstract

We construct two explicit Leray-Hirsch isomorphisms for torus equivariant oriented cohomology of flag varieties and give several applications. One isomorphism is geometric, based on Bott-Samelson classes. The other is algebraic, based on the description of the torus equivariant oriented cohomology of a flag variety as the dual of a formal affine Demazure algebra.