Suppose　that　Q　is　a　finite　quiver　and　G　subset　of　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/I,　where　I　is　an　arbitrary　ideal　of　path　algebra　kQ,　we　give　all　the　indecomposable　AG-modules　from　indecomposable　Lambda-modules　when　G　is　abelian.　In　particular,　we　apply　this　result　to　the　deformed　preprojective　algebra　Pi(lambda)(Q),　and　get　a　reflection　functor　for　the　module　category　of　Pi(lambda)(Q)G　Furthermore,　we　construct　a　new　quiver　Q(G)　and　prove　that　Pi(lambda)(Q)G　is　Morita　equivalent　to　Pi(eta)(QG)　for　some　eta.　(C)　2011　Elsevier　Inc.　All　rights　reserved.