Cohomology of infinite groups realizing fusion systems

Given a fusion system F defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G and prove a theorem which relates the cohomology of an infinite group model pi to the cohomology of the group G. We show that for the groups GL(n, 2), where n >= 5, the cohomology of the infinite group obtained using the Robinson model is different than the cohomology of the fusion system. We also discuss the signalizer functors P -> Theta(P) for infinite group models and obtain a long exact sequence for calculating the cohomology of a centric linking system with twisted coefficients.