Rigid local systems and motives of type G₂

Using the middle convolution functor MC_χ introduced by N.Katz, we prove the existence of rigid local systems whose monodromy is dense in the simple algebraic group G₂. We derive the existence of motives for motivated cycles which have a motivic Galois group of type G₂. Granting Grothendiecks standard conjectures, the existence of motives with motivic Galois group of type G₂ can be deduced, giving a partial answer to a question of Serre.