  The classical McKay correspondence establishes an explicit link from the
representation theory of a finite subgroup G of SU(2) and the geometry of the
minimal resolution of the quotient of the affine plane by G. In this paper we
discuss a possible generalization of the McKay correspondence to the case when
G is replaced with a cocompact discrete subgroup of the universal cover of
SU(1,1) such that its image in PSU(1,1) is a cocompact fuchsian group with
quotient of genus 0. We establish a correspondence between a certain class of
finite-dimensional unitary representations of G and vector bundles on an open
algebraic surface with the trivial canonical class canonically associated to G.
