  The article is a contribution to the local theory of geometric Langlands
correspondence. The main result is a categorification of the isomorphism
between the (extended) affine Hecke algebra, thought of as an algebra of
Iwahori bi-invariant functions on a semi-simple group over a local
non-Archimedian field, and Grothendieck group of equivariant coherent sheaves
on Steinberg variety of the Langlands dual group; 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 an earlier joint work with S. Arkhipov, it
relies on technical material developed in a paper with Z. Yun.
