Character varieties for real forms

Let $\Gamma$ be a finitely generated group and G a real form of SL(n,C). We propose a definition for the G-character variety of $\Gamma$ as a subset of the SL(n,C)-character variety of $\Gamma$. We consider two anti-holomorphic involutions of the SL(n,C)-character variety and show that an irreducible representation with character fixed by one of them is conjugate to a representation taking values in a real form of SL(n,C). We study in detail an example: the SL(n,C), SU(2,1) and SU(3) character varieties of the free product Z/3Z*Z/3Z.