Abstract: 
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 $H\subset G$.

1. Departamento de Matemáticas
   Facultad de Ciencias
   Universidad Nacional Autónoma de México
   04510, México, D.F., México