2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56461We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded as a result of a quantization procedure. The C*-algebra of the tangent groupoid of a given Lie groupoid G (with Lie algebra g) is the C*-algebra of a continuous field of C*-algebras over R with fibers A_0=C*(g)=C_0(g*) and A_h=C*(G) for nonzero h. The same is true for the corresponding reduced C*-algebras. Our results have applications to, e.g., transformation group C*-algebras, K-theory, and index theory.34 pages, minor correctionsMathematical PhysicsOperator AlgebrasQuantum AlgebraSymplectic Geometry46L65; 81S99text