It is well known that very special
–spaces and
grouplike –spaces
both model connective spectra. Both these models have equivariant analogues in the
case when the group acting is finite. Shimakawa defined the category of equivariant
–spaces and showed that
special equivariant –spaces
determine positive equivariant spectra. Costenoble and Waner [Trans.
Amer. Math. Soc. 326 (1991) 485-505] showed that grouplike equivariant
–spaces
determine connective equivariant spectra.
We show that with suitable model category structures the category of equivariant
–spaces
is Quillen equivalent to the category of equivariant
–spaces.
We define the units of equivariant ring spectra in terms of equivariant
–spaces
and show that the units of an equivariant ring spectrum determines a connective
equivariant spectrum.