#### Vol. 14, No. 4, 2020

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On the motivic class of an algebraic group

### Federico Scavia

Vol. 14 (2020), No. 4, 855–866
##### Abstract

Let $F$ be a field of characteristic zero admitting a biquadratic field extension. We give an example of a torus $G$ over $F$ whose classifying stack $BG$ is stably rational and such that $\left\{BG\right\}\ne {\left\{G\right\}}^{-1}$ in the Grothendieck ring of algebraic stacks over $F$. We also give an example of a finite étale group scheme $A$ over $F$ such that $B\phantom{\rule{-0.17em}{0ex}}A$ is stably rational and $\left\{B\phantom{\rule{-0.17em}{0ex}}A\right\}\ne 1$.

##### Keywords
motivic class, Grothendieck ring of stacks, classifying stack, algebraic torus
Primary: 14L15
Secondary: 14D23