This is from Segal's paper
Equivariant stable homotopy theory. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 59--63. Gauthier-Villars, Paris, 1971.
MR0423340 (54 #11319)
where he states that the equivariant stable cohomotopy of S is pi−astG(S)=bigoplusKpisast(B(NG(K)/K)+). In particular, pi0G(S) is the Burnside ring.
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