  Many interesting C*-algebras can be viewed as quantizations of Poisson
manifolds. I propose that a Poisson manifold may be quantized by a twisted
polarized convolution C*-algebra of a symplectic groupoid. Toward this end, I
define polarizations for Lie groupoids and sketch the construction of this
algebra. A large number of examples show that this idea unifies previous
geometric constructions, including geometric quantization of symplectic
manifolds and the C*-algebra of a Lie groupoid.
