Irreducible exotic ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$'s with free involutions

We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifo