<em>G</em>-Global Algebraic <em>K</em>-Theory

Abstract

We develop the foundations of G-global homotopy theory as a synthesis of classical equivariant homotopy theory on the one hand and global homotopy theory in the sense of Schwede on the other hand. Using this framework, we then introduce the G-global algebraic K-theory of small symmetric monoidal categories with G-action, unifying G-equivariant algebraic K-theory, as considered for example by Shimakawa, and Schwede's global algebraic K-theory.<br /> As an application of the theory, we prove that the G-global algebraic K-theory functor exhibits the category of small symmetric monoidal categories with G-action as a model of connective G-global stable homotopy theory, generalizing and strengthening a classical non-equivariant result due to Thomason. This in particular allows us to deduce the corresponding statements for global and equivariant algebraic K-theory.