For a given finite dimensional -algebra which admits a presentation in the form , where is an infinite group of -linear automorphisms of a locally bounded -category , a class of modules lying out of the image of the "push-down" functor associated with the Galois covering , is studied. Namely, the problem of existence and construction of the so called non-regularly orbicular indecomposable -modules is discussed. For a -atom (with a stabilizer ), whose endomorphism algebra has a suitable structure,a representation embedding , which yields large families of non-regularly orbicular indecomposable -modules,is constructed (Theorem 2.2). An important role in consideration is played by a result interpreting some class of -modules in terms of Cohen-Macaulay modules over certain skew grup algebra (Theorem 3.3). Also, Theorems 4.5 and 5.4, adapting the generalized tensor product construction and Galois covering scheme, respectively, for Cohen-Macaulay modules context, are proved and intensively used.
Piotr DOWBOR. "A construction of non-regularly orbicular modules for Galois coverings." J. Math. Soc. Japan 57 (4) 1077 - 1127, October, 2005. https://doi.org/10.2969/jmsj/1150287305