Discrete G-Spectra and embeddings of module spectra

In this paper we study the category of discrete G-spectra for a profinite group G. We consider an embedding of module objects in spectra into a category of module objects in discrete G-spectra, and study the relationship between the embedding and the homotopy fixed points functor. We also consider an embedding of module objects in terms of quasi-categories, and show that the two formulations of embeddings are equivalent in some circumstances.