### Equivariant orthogonal spectra and S-modules, by M. A. Mandell and J. P. May

The last few years have seen a revolution in our understanding of the
foundations of stable homotopy theory. Many symmetric monoidal model
categories of spectra whose homotopy categories are equivalent to the stable
homotopy category are now known, whereas no such categories were known before
1993. The most well-known examples are the category of S-modules and the
category of symmetric spectra. We focus on the category of orthogonal
spectra, which enjoys some of the best features of S-modules and symmetric
spectra and which is particularly well-suited to equivariant
generalization. We first complete the nonequivariant theory by comparing
orthogonal spectra to S-modules. We then develop the equivariant theory. For
a compact Lie group G, we construct a symmetric monoidal model category of
orthogonal G-spectra whose homotopy category is equivalent to the classical
stable homotopy category of G-spectra. We also complete the theory of
S_G-modules and compare the categories of orthogonal G-spectra and
S_G-modules. A key feature is the analysis of change of universe, change of
group, fixed point, and orbit functors in these two highly structured
categories for the study of equivariant stable homotopy theory.

M. A. Mandell <mandell@math.uchicago.edu>

J. P. May <may@math.uchicago.edu>