2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138183Many 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.60 pages. V3: Minor corrections including Def 4.4. Added details in sections 6.1 and 8.2. Additional references. Some signs changedSymplectic GeometryMathematical PhysicsOperator Algebras46L65; 53D17; 22A22, 53D50text