On the separability of the restriction functor

Let $G$ be a group, $\Lambda=\bigoplus_{\sigma \in G}\Lambda_{\sigma}$ a strongly graded ring by $G$, $H$ a subgroup of $G$ and $\Lambda_{H}=\bigoplus_{\sigma\in H}\Lambda_{\sigma}$. We give a necessary and sufficient condition for the ring $\Lambda/\Lambda_{H}$ to be separable, generalizing the corresponding result for the ring extension $\Lambda/\Lambda_{1}$. As a consequence of this result we give a condition for $\Lambda$ to be a hereditary order in case $\Lambda$ is a strongly graded by finite group $R$-order in a separable $K$-algebra, for $R$ a Dedekind domain with quotient field $K$.