Automorphism fixed points in the moduli space of semi-stable bundles

Given an automorphism tau of a smooth complex algebraic curve X, there is an induced action of the finite group G generated by tau on the moduli space \mathscr{M} of semi-stable rank-2 holomorphic bundles of fixed degree. We give a complete description of the fixed variety in terms of moduli spaces of parabolic bundles with flags and weights at the special orbits on the quotient curve X/G.