  We deal with a Lie group G acting by isometries on a Riemannian manifold M,
such that the quotient M/G is an orbifold, or, equivalently, all slice
representations are polar. We show that any smooth orbifold symmetric 2-tensor
on M/G lifts to a smooth G-invariant symmetric 2-tensor on M. The proof relies
on a fact about the Invariant Theory of finite reflection groups which may be
of independent interest.
