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Gushel-Mukai sixfolds are an important class of so-called Fano-K3 varieties.In this paper we show that they admit a multiplicative Chow-K\"unnethdecomposition modulo algebraic equivalence and that they have the Franchettaproperty. As side results, we show that double EPW sextics and cubes have theFranchetta property, modulo algebraic equivalence, and some vanishing resultsfor the Chow ring of Gushel-Mukai sixfolds.

Some Motivic Properties of Gushel-Mukai Sixfolds