  In a previous paper (joint with Hausel and Rodriguez-Villegas) we gave a
conjectural formula for the mixed Hodge polynomials of character varieties with
generic semisimple conjugacy classes at punctures and we prove a formula for
the E-polynomial. We also proved that these character varieties are
irreducible. In this paper we extend the above results to character varieties
with Zariski closures of arbitrary generic conjugacy classes at punctures
working with intersection cohomology. We also study Weyl group action on the
intersection cohomology of the partial resolutions of these character varieties
and give a conjectural formula for the two-variables polynomials that encode
the trace of the elements of the Weyl group on the subquotients of the weight
filtration. Finally, we compute the generating function of the stack count of
character varieties with Zariski closure of unipotent regular conjugacy class
at punctures.
