The motive of the classifying stack of the orthogonal group

TL;DR

This paper calculates the motive of the classifying stack of an orthogonal group within the Grothendieck ring of stacks, providing explicit algebraic invariants over fields with characteristic not equal to two.

Contribution

It offers the first explicit computation of the motive of the classifying stack of orthogonal groups in the Grothendieck ring of stacks.

Findings

Explicit motive of the classifying stack obtained

Results apply to fields with characteristic ≠ 2

Advances understanding of algebraic stacks and motives

Abstract

We compute the motive of the classifying stack of an orthogonal group in the Grothendieck ring of stacks over a field of characteristic different from two.