Twisted representations of vertex operator superalgebras

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This paper gives an analogue of Ag(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and Ag(V)-modules is established. It is proved that if V is g-rational, then Ag(V) is finite dimensional semisimple associative algebra and there are only finitely many irreducible g-twisted V-modules.