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We obtain general formulae expressing Hirzebruch genera of a manifold with Z=p-action in terms of invariants of this action (the sets of weights of flxed points). As an illustration, we consider numerous particular cases of well-known genera, in particular, the elliptic genus. We also describe the connection with the so-called Conner{Floyd equations for the weights of flxed points.

Calculation of Hirzebruch genera for manifolds acted on by the group Z / p via invariants of the action