  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 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 space M, thus generalizing the action studied by
Nakajima, Grojnowski and Baranovsky in cohomology.
