$G$-ANR's with homotopy trivial fixed point sets
Fundamenta Mathematicae 197 (2007), 1-16 MSC: 54C55, 55P91. DOI: 10.4064/fm197-0-1
Let $G$ be a compact group and $X$ a $G$-ANR. Then $X$ is a $G$-AR iff the $H$-fixed point set $X^H$ is homotopy trivial for each closed subgroup $H\subset G$.