Equivariant \(K\)-theory of generalized Steinberg varieties (Q742485)

The authors consider a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a complex reductive algebraic group and its nilpotent cone. They describe the equivariant \(K\)-groups of this family in terms of the extended affine Hecke algebra and double cosets in the extended affine Weyl group. This description is used to define Kazhdan-Lusztig ``bar'' involutions and Kazhdan-Lusztig bases for these equivariant \(K\)-groups.