Twisted gamma-filtration of a linear algebraic group

TL;DR

This paper introduces a twisted gamma-filtration on the Grothendieck group of a split simple algebraic group and uses it to construct torsion elements in related gamma-rings, advancing understanding of algebraic group structures.

Contribution

It develops a new twisted gamma-filtration on K_0(G) for split simple algebraic groups and applies it to construct torsion elements in gamma-rings of inner forms.

Findings

Defined the twisted gamma-filtration on K_0(G)

Constructed torsion elements in gamma-rings of inner forms

Provided new tools for studying algebraic group structures

Abstract

In the present notes we introduce and study the twisted gamma-filtration on K_0(G), where G is a split simple linear algebraic group over a field of characteristic prime to the order of the center of G. We apply this filtration to construct torsion elements in the gamma-ring of an inner form of the variety of Borel subgroups of G.