| Sumario: | For a discrete group G, we define the notion of G-II-algebra whose model is given by the graded group (πn(K))n≥1 corresponding to a topological space K on which G acts. This notion is a natural extension of the notion of II-algebra ([8]) and we use it to construct a spectral sequence relied to the II-algebra IImapGpt(X, Y), associated to the space of equivariant pointed continuous applications between two pointed G-CW-complexes X and Y. In particular, this spectral sequence converges to π*mapGpt(X, Y) when X is G-free and Y has only a finite number of non vanishing homotopy groups. We give an example obtained from the universal covering of BG.
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