  In this paper we develop the basic homotopy theory of G-symmetric spectra
(that is, symmetric spectra with a G-action) for a finite group G, as a model
for equivariant stable homotopy with respect to a G-set universe. This model
lies in between Mandell's equivariant symmetric spectra and the G-orthogonal
spectra of Mandell and May and is Quillen equivalent to the two. We further
discuss equivariant semistability, construct model structures on module,
algebra and commutative algebra categories and describe the homotopical
properties of the multiplicative norm in this context.
