The research project is implemented in the framework of H.F.R.I call “3rd Call for H.F.R.I.’s Research Projects to Support Faculty Members & Researchers. The objective of the project is to investigate questions that are encountered in the homological and homotopical theory of rings and modules, which are of interest mainly in algebra (module theory, representation theory) but also in geometry (group actions on spaces, algebraic geometry, tensor triangular geometry).