  We extend some results of Bonahon, Bullock, Turaev and Wong concerning the
skein algebras of closed surfaces to L^e's stated skein algebra associated to
open surfaces. We prove that the stated skein algebra with deforming parameter
+1 embeds canonically into the centers of the stated skein algebras whose
deforming parameter is an odd root unity. We also construct an isomorphism
between the stated skein algebra at +1 and the algebra of regular function of a
generalization of the SL2-character variety of the surface. As a result, we
associate to each isomorphism class of irreducible or local representations of
the stated skein algebra, an invariant which is a point in the character
variety.
