Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP_c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP_c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.