The main result of the paper is a formula for the fundamental group of the coarse moduli space of a topological stack. As an application, we find simple formulas for the fundamental group of the coarse quotient of a group action on a topological space in terms of the fixed point data. In particular, we recover, and vastly generalize, results of Armstrong, Bass, Higgins and Taylor and Rhodes.
"Fundamental groups of topological stacks with the slice property." Algebr. Geom. Topol. 8 (3) 1333 - 1370, 2008. https://doi.org/10.2140/agt.2008.8.1333