The homological multiplicative Orlov conjecture

Let $X$ and $X'$ be derived equivalent hyper-Kähler varieties, and let $h_{\mathrm{hom}}(X)$ denote the homological motive of $X$, equipped with its cup-product. The homological multiplicative Orlov conjecture. There is an isomorphism

$$(h_{\mathrm{hom}}(X),\cup)\simeq(h_{\mathrm{hom}}(X'),\cup).$$

This is the homological specialization of the multiplicative Orlov conjecture and is stated in the source to be wide open in higher dimension.