Free cyclic group actions on highly-connected $2n$-manifolds

In this paper we study smooth orientation-preserving free actions of the cyclic group $mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds, $sharp g (S^n times S^n)sharp Sigma$, where $Sigma$ is a homotopy $2n$-sphere. When $n=2$ we obtain a classification up to topological conjugation. When $n=3$ we obtain a classification up to smooth conjugation. When $n ge 4$ we obtain a classification up to smooth conjugation when the prime factors of $m$ are larger than a constant $C(n)$.