Liftings of pseudo-reflection groups of toric quotients of Krull schemes

Let $G$ be an affine algebraic group with a reductive identity component $G^0$ acting regularly on an affine Krull scheme $X=Spec(R)$ over an algebraically closed field. Let $T$ be an algebraic subtorus of $G$ and suppose that $Q(R{)}^T=Q(R^T)$ of quotient fields. We will show: If $G$ is the centralizer of $T$ in $G$, then the pseudo-reflections of the action of $G$ on $R^T$ can be lifted to those on $R$.