  The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler
manifold is restricted by integrality conditions. These restrictions can be
circumvented by passing to the universal covering space, provided that the lift
of the symplectic form is exact. I relate this construction to the Baum-Connes
assembly map and prove that it gives a strict quantization of the manifold. I
also propose a further generalization, classify the required structure, and
provide a means of computing the resulting algebras. These constructions
involve twisted group C*-algebras of the fundamental group which are determined
by a group cocycle constructed from the cohomology class of the symplectic
form.
