Dynamics on the PSL(2,C)-character variety of a twisted I-bundle

Let M be a twisted interval bundle over a nonorientable hyperbolizable surface. Let $X(M)$ be the PSL(2,C)-character variety of $\pi_1(M)$. We will discuss the dynamics of the action of $Out(\pi_1(M))$ on $X(M)$ and in particular find an open set on which the action is properly discontinuous that is strictly larger than the interior of the deformation space of marked hyperbolic manifolds homotopy equivalent to M. Further, we will identify which discrete and faithful representations can lie in a domain of discontinuity for this action.