Algebraic cycles and intersections of three quadrics

Let Y be a smooth complete intersection of three quadrics, and assume the dimension of Y is even. We show that Y has a multiplicative Chow-Kunneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers of) Y displays K3-like behaviour. As a by-product of the argument, we also establish a multiplicative Chow-Kunneth decomposition for double planes.