Geodesic
Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action
Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 515-548

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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. 
@article{IM2_1998_62_3_a3,
     author = {T. E. Panov},
     title = {Calculation of {Hirzebruch} genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action},
     journal = {Izvestiya. Mathematics },
     pages = {515--548},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a3/}
}
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T. E. Panov. Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action. Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 515-548. http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a3/