Kuznetsov–Shinder conjecture that D-equivalence implies L-equivalence

Let $X$ and $Y$ be smooth projective simply connected varieties. Two varieties are $D$-equivalent when there is a $k$-linear exact equivalence of their bounded derived categories of coherent sheaves, and $L$-equivalent when $\mathbb{L}^r([X]-[Y])=0$ in $K_0(\operatorname{Var}_k)$ for some positive integer $r$, where $\mathbb{L}=[\mathbb{A}^1_k]$.

Kuznetsov–Shinder conjecture. If $X$ and $Y$ are $D$-equivalent, then they are $L$-equivalent:

$$\mathcal{D}^{b}(X)\simeq\mathcal{D}^{b}(Y)\implies X\sim_LY.$$

The conjecture connects derived categories with motivic equivalence. It is refuted by the paper from which this statement is taken, which constructs a counterexample using moduli spaces of sheaves on K3 surfaces.