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We show that a wide range of Fano varieties of K3 type, recently constructedby Bernardara, Fatighenti, Manivel and Tanturri, have a multiplicativeChow-K\"unneth decomposition, in the sense of Shen-Vial. It follows that theChow ring of these Fano varieties behaves like that of K3 surfaces. As a sideresult, we obtain some criteria for the Franchetta property of blown-upprojective varieties.

On the Chow Ring of Fano Fourfolds of K3 type