  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 $\{BG\}\{G\}\neq 1$ in the Grothendieck
ring of algebraic stacks over $F$. We also give an example of a finite \'etale
group scheme $A$ over $F$ such that $BA$ is stably rational and $\{BA\}\neq 1$.
