Motives and cycles of geometrically rational varieties

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The theory of (Chow-)motives has been introduced by one of the most famous mathematicians of the last century, Alexander Grothendieck (winner of the Fields medal -- the analog of the Nobel price for mathematics -- in 1966). This is an universal theory which explains almost all existing algebraic objects, as for instance quadratic forms, elliptic curves, or algebraic surfaces. Most of these (algebraic) objects play an essential role in algebraic coding theory or cryptography.