  Suppose that $Q$ is a finite quiver and $G\subseteq \Aut(Q)$ is a finite
group, $k$ is an algebraic closed field whose characteristic does not divide
the order of $G$. For any algebra $\Lambda=kQ/{\mathcal {I}}$, $\mathcal {I}$
is an arbitrary ideal of path algebra $kQ$, we give all the indecomposable
$\Lambda G$-modules from indecomposable $\Lambda$-modules when $G$ is abelian.
In particular, we apply this result to the deformed preprojective algebra
$\Pi_{Q}^{\lambda}$, and get a reflection functor for the module category of
$\Pi_{Q}^{\lambda}G$. Furthermore, we construct a new quiver $Q_{G}$ and prove
that $\Pi_{Q}^{\lambda}G$ is Morita equivalent to $\Pi_{Q_{G}}^{\eta}$ for some
$\eta$.
