Equivariant K-theory of flag varieties revisited and related results

We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring KT(G/B) of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in KT(G/B) to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of K(X)Q where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of Schubert varieties in the Grothendieck ring of G/B. © Instytut Matematyczny PAN, 2013.