2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221695Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction.34 pages; to appear in American Journal of MathematicsSymplectic GeometryDifferential Geometry53D17; 53D20text