Given a group G of k-linear automorphisms of a locally bounded k-category R, the problem of existence and construction of non-orbicular indecomposable R/G-modules is studied. For a suitable finite sequence B of G-atoms with a common stabilizer H, a representation embedding ${\Phi }^B:Iₙ-spr\left(H\right)\to mod(R/G)$, which yields large families of non-orbicular indecomposable R/G-modules, is constructed (Theorem 3.1). It is proved that if a G-atom B with infinite cyclic stabilizer admits a non-trivial left Kan extension B̃ with the same...