Many important equivariant theories naturally exist not only for a particular group, but
in a uniform way for a family of groups. Prominent examples are equivariant stable homotopy
theory, equivariant K-theory and equivariant bordism. This observation led to the birth of global
homotopy theory. Globalness is a measure of the naturalness of a cohomology theory. Schwede
developed a modern approach of it by global orthogonal spectra, which is inspired by Greenlees
and May.
So far several models of global homotopy theory have been established with different
motivations and advantages, including Bohmann's model, Gepner's model and Rezk's model. We
construct a new global homotopy theory, almost global homotopy theory, which is equivalent to
the previous models. But with it we can show that quasi-theories can be globalized if the original
cohomology theory can be globalized. This leads to the conjecture that the globalness of a
cohomology theory is determined by the formal component of its divisible group; when the etale
component varies, the globalness does not change.

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