Question: Is there a group $G$ and a CW-complex $X$ such that
$X$ is homotopy equivalent to the circle $S^{1}$.
$G$ acts on $X$
the space fixed points $X^{G}$ is weakly equivalent to $S^{2}$ ?
Question: Is there a group $G$ and a CW-complex $X$ such that
$X$ is homotopy equivalent to the circle $S^{1}$.
$G$ acts on $X$
the space fixed points $X^{G}$ is weakly equivalent to $S^{2}$ ?