For a given finite dimensional $k$ -algebra $A$ which admits a presentation in the form $R/G$ , where $G$ is an infinite group of $k$ -linear automorphisms of a locally bounded $k$ -category $R$ , a class of modules lying out of the image of the "push-down" functor associated with the Galois covering $R\to R/G$ , is studied. Namely, the problem of existence and construction of the so called non-regularly orbicular indecomposable $R/G$ -modules is discussed. For a $G$ -atom $B$ (with a stabilizer $G_B$ ), whose endomorphism algebra has a suitable structure,a representation embedding $\Phi^{B(f,s)}{}_{|}:I_n-\mathrm{spr}_{l(s)}(kG_B)\to \mathrm{mod}(R/G)$ , which yields large families of non-regularly orbicular indecomposable $R/G$ -modules,is constructed (Theorem 2.2). An important role in consideration is played by a result interpreting some class of $R/G$ -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.