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

We obtain general formulae expressing Hirzebruch genera of a manifold with $\mathbf Z/p$-action in terms of invariants of this action (the sets of weights of fixed 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 fixed points.