Given a finite group , we develop a theory of -equivariant noncommutative motives. This theory provides a well-adapted framework for the study of -schemes, Picard groups of schemes, -algebras, -cocycles, -equivariant algebraic -theory, etc. Among other results, we relate our theory with its commutative counterpart as well as with Panin’s theory. As a first application, we extend Panin’s computations, concerning twisted projective homogeneous varieties, to a large class of invariants. As a second application, we prove that whenever the category of perfect complexes of a -scheme admits a full exceptional collection of -invariant (-equivariant) objects, the -equivariant Chow motive of is of Lefschetz type. Finally, we construct a -equivariant motivic measure with values in the Grothendieck ring of -equivariant noncommutative Chow motives.
"Equivariant noncommutative motives." Ann. K-Theory 3 (1) 125 - 156, 2018. https://doi.org/10.2140/akt.2018.3.125