Abstract
Using bundles over Grassmannians, we construct a category of spectra which underlies Boardman's stable category, has itself a symmetric monoidal smash product, and which produces RO( G)-graded equivariant cohomology theories from group actions on spectra. May's vast array of categories of spectra embed in our single category, and a variety of adjoint functors allow us to deduce properties of our category from those of his. The construction of these functors forces us to develop a theory of parametrized spaces and spectra as well.
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