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Let $k$ be a perfect field. Let $GL_n$ be the general linear group over $k$. Does anybody know a reference for the computation of the motive $$ M(GL_n) $$ in Voevodsky's category $DM(k)$?

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The motive of a split reductive group over a perfect field has been computed by Shahram Biglari in: Motives of reductive groups. Amer. J. Math. 134 (2012), pp.235--257.

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