  For an aspherical symplectic manifold, closed or with convex contact
boundary, and with vanishing first Chern class, a Floer chain complex is
defined for Hamiltonians linear at infinity with coefficients in the group ring
of the fundamental group. For two non-degenerate Hamiltonians of the same slope
continuation maps are shown to be simple homotopy equivalences. As a corollary
the number of contractible Hamiltonian orbits of period 1 can be bounded from
below.
