  Let $M$ be a compact nonnegatively curved Riemannian manifold admitting an
isometric action by a compact Lie group $\mathsf G$ in a way that the quotient
space $M/\mathsf G$ has nonempty boundary. Let $\pi : M \to M/\mathsf G$ denote
the quotient map and $B$ be any boundary stratum of $M/\mathsf G$. Via a
specific soul construction for $M/ \mathsf G$ we construct a smooth closed
submanifold $N$ of $M$ such that $M \setminus \pi^{-1}(B)$ is diffeomorphic to
the normal bundle of $N$. As an application we show that a simply connected
torus manifold admitting an invariant metric of nonnegative curvature is
rationally elliptic.
