Transfers generate the equivariant stable homotopy category

Abstract

Let G be a compact Lie group. In the corresponding equivariant stable homotopy category, whose morphisms are classes represented by maps of pairs ( N, N − 0) × X → ( M, M − 0) × Y, where M and N are real finite dimensional G-modules, one proves that any of these morphisms X → Y factors as a composite X → τ V → ψ Y , where τ(ƒ) is the transfer of a fixed point situation over X, N × E ⊃ V → ƒ M × E and Ψ: V → Y is an equivariant map in the usual sense (nonstable).