A motivic global Torelli theorem for isogenous K3 surfaces

We prove that the Chow motives of twisted derived equivalent K3 surfaces are isomorphic, not only as (due to Huybrechts), but also Frobenius algebra objects. Combined with a recent result Huybrechts, we conclude two complex projective isogenous (i.e. their second rational cohomology groups Hodge isometric) if and isomorphic objects; this can be regarded motivic Torelli-type theorem. ask whether, more generally, hyper-Kähler varieties have (Frobenius) objects in particular graded algebras. In appendix, justify introducing notion “Frobenius object” by showing existence an infinite family whose pairwise non-isomorphic particular, non-isogenous