G∞–ring spectra and Moore spectra for β–rings

In this paper, we introduce the notion of $G_\infty$-ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their and cohomology groups. We illustrate structure by analysing when Moore spectrum can be endowed structure. Such $G_\infty$-structures correspond underlying ring, indexed Burnside ring. exhibit close relation between these $\beta$-ring, thus providing new perspective theory $\beta$-rings.