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

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 split reductive group over field k characteristic 0. More precisely, extend such respective T-equivariant (T maximal torus G) theories, and then them using equivariant Schubert calculus techniques. This generalizes an approach suggested by Garibaldi-Petrov-Semenov for Steenrod operations. As application establish Riemann-Roch type formula Hecke action theories additive type.