On the cohomology of orbit space of free \pmb{${\text{ZZ}}_p$}-actions on lens spaces

Let $G={\text{ZZ}}_p$, $p$ an odd prime, act freely on a finite-dimensional CW-complex $X$ with mod $p$ cohomology isomorphic to that of a lens space $L^{2m-1}(p;q_1,\mathrm{.}\mathrm{.}\mathrm{.},q_m)$. In this paper, we determine the mod $p$ cohomology ring of the orbit space $X\mathrm{/}G$, when $p^2\nmid m$.