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If G is a group acting properly by semisimple isometries on a proper CAT(0)space X, then we build models for the classifying spaces E_{vc} and E_{fbc}under the additional assumption that the action of G has a well-behavedcollection of axes in X. (This hypothesis is described in the paper.) Weconjecture that the latter hypothesis is satisfied in a large range of cases.Our classifying spaces resemble those created by Connolly, Fehrman, andHartglass for crystallographic groups G.

Constructions of E_{vc} and E_{fbc} for groups acting on CAT(0) spaces