Flat and Stably Flat Modules

We study Krophollerʹs generalisation of Lazardʹs criterion for a module to be flat. The context is complete cohomology and modules of type (FP)∞. Let G be a group in the class 1 of groups which act on a finite dimensional contractible cell complex with finite stabilisers and let R be a strongly G-graded algebra. We provide a characterisation of the stably flat R-modules under the assumption that R1 is coherent of finite global dimension.