  Let M be a smooth and compact moduli space of stable coherent sheaves on a
projective surface S with an effective (or trivial) anti-canonical line bundle.
We find generators for the cohomology ring of M, with integral coefficients.
When S is simply connected and a universal sheaf E exists over SxM, then its
class [E] admits a Kunneth decomposition as a class in the tensor product of
the topological K-rings K(S) and K(M). The generators are the Chern classes of
the Kunneth factors of [E] in K(M). The general case is similar
