  Let R be the skew group algebra of a finite group acting on the path algebra
of a quiver. This article develops both theoretical and practical methods to do
computations in the Morita reduced algebra associated to R. Reiten and
Riedtmann proved that there exists an idempotent e of R such that the algebra
eRe is both Morita equivalent to R and isomorphic to the path algebra of some
quiver which was described by Demonet. This article gives explicit formulas for
the decomposition of any element of eRe as a linear combination of paths in the
quiver described by Demonet. This is done by expressing appropriate
compositions and pairings in a suitable monoidal category which takes into
account the representation theory of the finite group.
