In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a "categorical version" of Kazhdan-Lusztig- Ginzburg's con- struction of the affine Hecke algebra, and is used in particular by the first author and I. Mirkovi? in the course of the proof of Lusztig?s conjectures on equivariant K-theory of Springer fibers.
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