Fu–Vial's multiplicative Orlov conjecture

Let $X$ and $X'$ be derived equivalent hyper-Kähler varieties. The Chow motive $h(X)$ is equipped with its cup-product structure, written $(h(X),\cup)$. Fu–Vial's multiplicative Orlov conjecture. There is an isomorphism of Chow motives respecting the cup-product,

$$(h(X),\cup)\simeq(h(X'),\cup).$$

This strengthens Orlov's conjecture by requiring compatibility with multiplication. It is known for K3 surfaces, while the higher-dimensional case remains open.