When is the representation ring of neutral component of reductive group flat?

Question

Let $G$ be a reductive complex algebraic group, not necessarily connected. Let $G^\circ$ be the connected component of the identity. When is it true that $R(G^\circ)$ is flat over each connected component of $\mathrm{Spec}(R(G))$? Here $R(G)$ is the representation ring of $G$.