  In this article we study Whitney (B) regular stratified spaces with the
action of a compact Lie group $G$ which preserves the strata. We prove an
equivariant submersion theorem and use it to show that such a $G$-stratified
space carries a system of $G$-equivariant control data. As an application, we
show that if $A \subset X$ is a closed $G$-stratified subspace which is a union
of strata of $X$, then the inclusion $i : A \hookrightarrow X$ is a
$G$-equivariant cofibration. In particular, this theorem applies whenever $X$
is a $G$-invariant analytic subspace of an analytic $G$-manifold $M$ and $A
\hookrightarrow X$ is a closed $G$-invariant analytic subspace of $X$.
