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Suppose that one has a Shimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a moduli space of motives (e.g. PEL type Shimura variety, but also Hodge type and abelian type Shimura varieties). What is the relation between $G$ and the motivic Galois group (?) of the category of motives parametrized by $Sh(G,X)$?

(References for the exact definition of motivic Galois group being used in the answer would also be appreciated).


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Dear unknown, you seem not to have chosen the best possible introduction to your question... It does not suggest that you will appreciate an eventual proficient answer (that I do not possess). – monodromy Nov 5 '11 at 23:04

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