  Let M be a weakly monotone symplectic manifold, and H be a time-dependent
Hamiltonian; we assume that the periodic orbits of the corresponding
time-dependent Hamiltonian vector field are non-degenerate. We construct a
refined version of the Floer chain complex associated to these data and any
regular covering of M, and derive from it new lower bounds for the number of
periodic orbits. We prove in particular that if the fundamental group of M is
finite and solvable or simple, then the number of periodic orbits is not less
than the minimal number of generators of the fundamental group. For a general
closed symplectic manifold with infinite fundamental group, we show the
existence of 1-periodic orbit of Conley-Zehnder index 1-n for any
non-degenerate 1-periodic Hamiltonian system.
