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We prove the equivalence between the categories of motives of rigid analyticvarieties over a perfectoid field $K$ of mixed characteristic and over theassociated (tilted) perfectoid field $K^{\flat}$ of equal characteristic. Thiscan be considered as a motivic generalization of a theorem of Fontaine andWintenberger, claiming that the Galois groups of $K$ and $K^\flat$ areisomorphic. A main tool for constructing the equivalence is Scholze's theory ofperfectoid spaces.

A motivic version of the theorem of Fontaine and Wintenberger