The K-ring of Steinberg varieties

In the upcoming series of talks we discuss some equivalences by Bezrukavnikov between categories of coherent sheaves on Steinberg varieties and of perverse sheaves on the affine flag variety. In this talk I discuss the decategorified isomorphism preceeding Bezrukavnikov’s equivalence of categories. This is a ring isomorphism of the KK-ring of the Steinberg variety under convolution and the affine Hecke algebra originally due to Kazhdan, Lusztig and Ginzburg.