  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 equivariant homotopy and cohomology groups.
We illustrate this structure by analysing when a Moore spectrum can be endowed
with a $G_\infty$-ring structure. Such $G_\infty$-structures correspond to
power operations on the underlying ring, indexed by the Burnside ring. We
exhibit a close relation between these globally equivariant power operations
and the structure of a $\beta$-ring, thus providing a new perspective on the
theory of $\beta$-rings.
