  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 (\cite{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 ({\it cf.} \cite{Ko,Do}). As a
consequence of our results, we get quantization of modified classical dynamical
$r$-matrices over abelian bases in the reductive case
