Representations of surface groups with finite mapping class group orbits

Let (S, *) be a closed oriented surface with a marked point, let G be a fixed group, and let rho: pi(1)(S) -> G be a representation such that the orbit of rho under the action of the mapping class group Mod(S, *) is finite. We prove that the image of rho is finite. A similar result holds if pi(1)(S) is replaced by the free group F-n on n >= 2 generators, and where Mod(S, *) is replaced by Aut(F-n). We show that if G is a linear algebraic group and if the representation variety of pi(1)(S) is replaced by the character variety, then there are infinite image representations which are fixed by the whole mapping class group.