Classical shadows of stated skein representations at roots of unity

We extend some results of Bonahon, Wong, Bullock and Turaev concerning the skein algebras of closed surfaces to L's stated skein algebras associated to open surfaces.We prove that the stated skein algebra with deforming parameter C1 embeds canonically into the center of the stated skein algebra whose deforming parameter is an odd root unity.We also construct an isomorphism between the stated skein algebra at C1 and the algebra of regular functions of the relative SL 2 -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 relative character variety.57R56