Smooth quotients of complex tori by finite groups

Let $A$ be a complex torus and $G$ finite group acting on without translations such that $A/G$ is smooth. Consider the subgroup $F\leq G$ generated by elements have at least one fixed point. We prove there exists point $x\in A$ whole $F$ quotient fibration of products projective spaces over an \'etale (the being Galois with $G/F$). In particular, when $G=F$, we may assume fixes origin. This related to previous work authors, where case actions abelian varieties fixing origin was treated. Here, generalize these results tori use them reduce problem classifying smooth quotients quotients. An ingredient proof our fixed-point theorem result proving in every irreducible reflection element which not contained any proper Coxeter this property for well-generated groups. proved Stephen Griffeth appendix.