Résumé
Le$X$be a$C^\infty$ -manifold and$\g$be a finite dimensional Lie algebra acting freely on$X$ . Let$r \in \ve^2(\g)$be such that$Z=[r,r] \in \ve^3(\g)^\g$ . In this paper we prove that every quasi-Poisson$(\g,Z)$ -manifold can be quantized. This is a generalization of the existence of a twist quantization of coboundary Lie bialgebras (EH) in the case$X=G$(where$G$is the simply connected Lie group corresponding to$\g$ ). We deduce our result from a generalized formality theorem. In the case Z=0, we get a new proof of the existence of (equivariant) formality theorem and so (equivariant) quantization of Poisson manifold (ıt cf. Ko,Do). As a consequence of our results, we get quantization of modified classical dynamical$r$ -matrices over abelian bases in the reductive case