The fundamental group of quotients of products of some topological spaces by a finite group -- A generalization of a Theorem of Bauer-Catanese-Grunewald-Pignatelli

We provide a description of the fundamental group of the quotient of a product of topological spaces $X_i$, each admitting a universal cover, by a finite group $G$, provided that there is only a finite number of path-connected components in $X_i^g$ for every $g\in G$. This generalizes previous work of Bauer-Catanese-Grunewald-Pignatelli and Dedieu-Perroni.