  Let $G$ be a Poisson Lie group and $\g$ its Lie bialgebra. Suppose that $\g$
is a group Lie bialgebra. This means that there is an action of a discrete
group $\Gamma$ on $G$ deforming the Poisson structure into coboundary
equivalent ones. Starting from this we construct a non-trivial stack of
Hopf-Poisson algebras and prove the existence of associated deformation
quantizations. This non-trivial stack is a stack of functions on the formal
Poisson group, dual of the starting $\Gamma$ Poisson-Lie group. To quantize
this non-trivial stack we use quantization of a $\Gamma$ Lie bialgebra which is
the infinitesimal of a $\Gamma$ Poisson-Lie group (cf \cite{MS} for simple Lie
groups and $\Gamma$ a covering of the Weyl group and \cite{EH} for quantization
in the general case).
