HECKE CORRESPONDENCES FOR SMOOTH MODULI SPACES OF SHEAVES

We define functors on the derived category of the moduli space M of stable sheaves on a smooth projective surface (under Assumptions A and S below), and prove that these functors satisfy certain commutation relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the K-theory of the moduli spaceM, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.