Abstract
We introduce the notion of Frobenius-friendly categories and obtain the slash functors on these categories. Let G be a finite p-group. We give a local construction of the -stable category of a big enough Frobenius-friendly category of -modules: an endopermutation -module in gives rise, via slash functors, to a family of endopermutation -modules, where Q runs over non-trivial subgroups of G, together with certain isomorphisms. Conversely, the data of a suitable compatible family of endopermutation -modules comes from an endopermutation -module in unique up to isomorphism in the -stable category.
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