  A Lie group G in a group pair (D,G), integrating a Lie algebra g in a Manin
pair (d,g) has a quasi-Poisson structure. We define the quasi-Poisson actions
of such Lie groups G, that generalize the Poisson actions of Poisson Lie
groups. We define and study the moment maps for those quasi-Poisson actions
which are quasi-hamiltonian. These moment maps take values in the homogeneous
space D/G. We prove an analogue of the hamiltonian reduction theorem for
quasi-Poisson group actions, and we study the symplectic leaves of the orbit
spaces of quasi-hamiltonian spaces.
