  Let $G$ be a Lie group and $M$ a smooth proper $G$-manifold. Let $pi:Mto M/G$
denote the natural map to the orbit space. Then there exist a PL manifold $P$,
a polyhedron $L$ and homeomorphisms $tau:Pto M$ and $\sigma:M/Gto L$ such that
$\sigma\circpi\circ\tau$ is PL. If $M$ and the $G$-action are of analytic
class, we can choose subanalytic $\tau$ and then unique $P$ and $L$.
