Résumé
We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g, r, Z). We derive from this that the formal Poisson manifolds g* and G* are isomorphic, and we construct an injective algebra morphism S(g*)(g) hooked right arrow U(g*). When (g, r, Z) can be quantized, we construct a deformation of this morphism. In the particular case when g is quasitriangular and nondegenerate, we compare our construction with Semenov-Tian-Shansky's construction of a commutative subalgebra of U(g*). We also show that the canonical derivation of the function ring of G* is Hamiltonian.