  Given a Calabi-Yau manifold $X$ acted by a group $G$ and considering the
$B$-branes on $X$ as objects in the derived category of coherent sheaves, we
give a definition of equivariant branes, which generalizes the concept of
equivariant sheaves. We also propose a definition of equivariant charge of an
equivariant brane. The spaces of strings joining the branes ${\mathcal F}$ and
${\mathcal G}$, are the groups $Ext^i({\mathcal F},\,{\mathcal G})$. We prove
that the spaces of strings between two $G$-equivariant branes support
representations of $G$. Thus, these spaces can be decomposed in direct sum of
invariant spaces for the $G$-action. We show some particular decompositions,
when $X$ is a toric variety and when $X$ is a flag manifold of a semisimple Lie
group.
