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It is well known that very special Γ–spaces and grouplike E∞–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 Γ–spaces
and showed that special equivariant Γ–spaces determine positive equivariant
spectra. Costenoble and Waner [Trans. Amer. Math. Soc. 326 (1991) 485-505]
showed that grouplike equivariant E∞–spaces determine connective equivariant
spectra.
We show that with suitable model category structures the category of equivariant
Γ–spaces is Quillen equivalent to the category of equivariant E∞–spaces. We define
the units of equivariant ring spectra in terms of equivariant Γ–spaces and show that
the units of an equivariant ring spectrum determines a connective equivariant
spectrum.
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