In my talk I shall explain our with Kaoru Ono construction of Floer-Novikov cohomology groups $HFN^* (M^{\Gamma_\xi \times H},\xi, Q)$ defined on a regular covering $M^{\Gamma_\xi \times H}$ of a compact symplectic manifold $(M, \omega)$ with transformation group $\Gamma_\xi \times H$ and associated to a locally symplectic isotopy ${\{\varphi_t\}}$ of $(M, \omega)$ with flux $\xi \in H ^1 (M, R)$. Then $H$ acts naturally on $HFN^* (M^{\Gamma_\xi \times H},\xi, Q)$. For a subgroup $G \subset H$ denote by $(HFN^* (M^{\Gamma_\xi \times H},\xi, Q))^G$ the subgroup of $HFN^* (M^{\Gamma_\xi \times H}, \xi, Q)$ consisting of the fixed points of the $G$-action. We prove that the rank of $(HFN^* (M ^{\Gamma_\... more