Coadjoint orbits of Lie groupoids

For a Lie groupoid G with Lie algebroid A, we realize the symplectic leaves of the Lie-Poisson structure on A∗ as orbits of the affine coadjoint action of the Lie groupoid JG⋉T∗M on A∗, which coincide with the groupoid orbits of the symplectic groupoid T∗G over A∗. It is also shown that there is a fiber bundle structure on each symplectic leaf. In the case of gauge groupoids, a symplectic leaf is the universal phase space for a classical particle in a Yang-Mills field.