What is "g-spectrum"

In algebraic topology, a G-spectrum is a spectrum with an action of a (finite) group.

Let X be a spectrum with an action of a finite group G. The important notion is that of the homotopy fixed point set X. There is always

X → X, 
a map from the fixed point spectrum to a homotopy fixed point spectrum (because, by definition, X is the mapping spectrum F(BG, X).)

Example: Z/2 acts on the complex K-theory KU by taking the conjugate bundle of a complex vector bundle. Then KU = KO, the real K-theory.

The cofiber of X → X is called the Tate spectrum of X.