Localized operations on T-equivariant oriented cohomology of projective homogeneous varieties

Abstract

In the present paper we provide a general algorithm to compute multiplicative cohomological operations on algebraic oriented cohomology of projective homogeneous G -varieties, where G is a split reductive algebraic group over a field k of characteristic 0. More precisely, we extend such operations to the respective T -equivariant ( T is a maximal split torus of G ) oriented theories, and then compute them using equivariant Schubert calculus techniques. This generalizes an approach suggested by Garibaldi-Petrov-Semenov for Steenrod operations. As an application we establish the Riemann-Roch type formula for the Hecke action on theories of additive type.