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In algebraic topology, a G-spectrum is a spectrum with an action of a 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 h G {\displaystyle X^{hG}}. There is always

a map from the fixed point spectrum to a homotopy fixed point spectrum G {\displaystyle F^{G}}.]

Example: Z / 2 {\displaystyle \mathbb {Z} /2} acts on the complex K-theory KU by taking the conjugate bundle of a complex vector bundle. Then K U h Z / 2 = K O {\displaystyle KU^{h\mathbb {Z} /2}=KO} , the real K-theory.

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