The first step in the fundamental Clifford theoretic approach
to general block theory of finite groups reduces to: $H$ is
a subgroup of the finite group $G$ and $e$ is a central idempotent
of $H$ such that $e({}^{g}e)=0$ for all $g \in G-H$.
Then $\Tr_{H}^{G}(e)$ is a central idempotent of $G$ and
induction from $H$ to $G$, $\Ind_{H}^{G}$, is part
of a Morita equivalence between the categories of $e$-modules
and of $\Tr_{H}^{G}(e)$-modules. Let $W$ be an indecomposable
$e$-module, so that $V=\Ind_{H}^{G}(W)$ is an indecomposable
$\Tr_{H}^{G}(e)$-module. We present results that relate the
Green correspondents of $W$ and $V$ via induction and restriction.