  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 examine the
dynamics of the action of Out(\pi_1(M)) on X(M), and in particular, we 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 identify which discrete and faithful
representations can lie in a domain of discontinuity for the action of
Out(\pi_1(M)) on X(M).
