Chen–Ruan cohomology of some moduli spaces of parabolic vector bundles

Let (X,D) be an ℓ-pointed compact Riemann surface of genus at least two. For each point x∈D, fix parabolic weights such that . Fix a holomorphic line bundle ξ over X of degree one. Let PMξ denote the moduli space of stable parabolic vector bundles, of rank two and determinant ξ, with parabolic structure over D and parabolic weights . The group of order two line bundles over X acts on PMξ by the rule E∗⊗L↦E∗⊗L. We compute the Chen–Ruan cohomology ring of the corresponding orbifold.