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Abstract:  Let G be a simple and simply connected algebraic group over \(\Bbb C\). We can attach to G the sheaf of conformal blocks: a vector bundle on M_g whose fibres are identified with global sections of a certain line bundle on the stack of G-torsors. We generalize the construction of conformal blocks to the case in which \(\cal G\) is a twisted group over a curve which can be defined in terms of covering data. In this case the associated conformal blocks define a sheaf on a Hurwitz space and have properties analogous to the classical case.