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We prove that if a smooth projective algebraic variety of dimension less orequal to three has a unit type integral $K$-motive, then its integral Chowmotive is of Lefschetz type. As a consequence, the integral Chow motive is ofLefschetz type for a smooth projective variety of dimension less or equal tothree that admits a full exceptional collection.

Integral Chow motives of threefolds with $K$-motives of unit type