  We discuss a framework for quantizing a Poisson manifold via the quantization
of its symplectic groupoid, that combines the tools of geometric quantization
with the results of Renault's theory of groupoid C*-algebras. This setting
allows very singular polarizations. In particular we consider the case when the
modular function is "multiplicatively integrable", i.e. when the space of
leaves of the polarization inherits a groupoid structure. If suitable
regularity conditions are satisfied, then one can define the quantum algebra as
the convolution algebra of the subgroupoid of leaves satisfying the
Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of
Poisson structures on CP_n, seen as Poisson homogeneous spaces of the standard
Poisson-Lie group SU(n+1). We show that a bihamiltoniam system on CP_n defines
a multiplicative integrable model on the symplectic groupoid; we compute the
Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for
applying Renault theory. We recover and extend Sheu's description of quantum
homogeneous spaces as groupoid C*-algebras.
