Abstract
The article is a contribution to the local theory of geometric Langlands duality. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra associated to a reductive group $G$ and Grothendieck group of equivariant coherent sheaves on Steinberg variety of Langlands dual group ${G\check { }}$ ; this isomorphism due to Kazhdan–Lusztig and Ginzburg is a key step in the proof of tamely ramified local Langlands conjectures. The paper is a continuation of the author’s joint work with Arkhipov, it relies on the technical material developed in a joint work with Yun.
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