Orbifold products for higher K-theory and motivic cohomology

TL;DR

This paper extends the theory of orbifold Chow and K-theory rings to higher Chow groups and higher algebraic K-theory, broadening the algebraic and geometric understanding of orbifolds.

Contribution

It introduces a natural extension of orbifold products to higher K-theory and motivic cohomology, building on prior foundational work.

Findings

Construction of orbifold products for higher K-theory.

Relation between higher Chow groups and K-theory via orbifold Chern character.

Generalization of orbifold cohomology to higher algebraic structures.

Abstract

Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them by the orbifold Chern character map, generalizing the fundamental work of Chen-Ruan on orbifold cohomology. In this paper, we extend this theory naturally to higher Chow groups and higher algebraic K-theory, mainly following the work of Jarvis-Kaufmann-Kimura and Edidin-Jarvis-Kimura.