Global algebraic K-theory (1912.08872v2)

Abstract: We introduce a global equivariant refinement of algebraic K-theory; here global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global $\Omega$-spectrum that keeps track of genuine $G$-equivariant infinite loop spaces, for all finite groups $G$. The resulting global algebraic K-theory spectrum is a rigid way of packaging the representation K-theory, orSwan K-theory' into one highly structured object.