  We study various aspects of Fedosov star-products on symplectic manifolds. By
introducing the notion of "quantum exponential maps", we give a criterion
characterizing Fedosov connections. As a consequence, a geometric realization
is obtained for the equivalence between an arbitrary *-product and a Fedosov
one. Every Fedosov *-product is shown to be a Vey *-product. Consequently, one
obtains that every *-product is equivalent to a Vey * -product, a classical
result of Lichnerowicz. Quantization of a hamiltonian G-space, and in
particular, quantum momentum maps are studied. Lagrangian submanifolds are also
studied under a deformation quantization.
