Continuous group actions on profinite spaces

For a profinite group, we construct a model structure on profinite spaces and profinite spectra with a continuous action. This yields descent spectral sequences for the homotopy groups of homotopy fixed point spaces and for stable homotopy groups of homotopy orbit spaces. our main example is the Galois action on profinite etale topological types of varieties over a field. One motivation is to understand Grothendieck's section conjecture in terms of homotopy fixed points. (C) 2010 Elsevier B.V. All rights reserved.