Cancellation conjecture for the Lefschetz motive

Let $k$ be a field, let $K_0(\operatorname{Var}_k)$ be the Grothendieck ring of varieties over $k$, and let $\mathbb{L}=[\mathbb{A}^1_k]$ be the Lefschetz class. Cancellation conjecture for the Lefschetz motive. The element $\mathbb{L}$ is not a zero divisor in $K_0(\operatorname{Var}_k)$. This is presented as a second well-known conjecture about the Grothendieck ring and is used in the paper as an alternative conditional hypothesis for the failure of motivic stabilization; the source gives no resolution.