Motives with Galois group of type G2:: an exceptional theta-correspondence

In this paper, we study an exceptional theta correspondence, obtained by restricting the minimal automorphic representation of the adjoint group of type E-7 and rank 3 over Q to the dual pair G x PGSp(6). Here G is the anisotropic form of G(2) over Q; using the correspondence, we lift certain automorphic forms on G to holomorphic cusp forms on PGSp(6). This Lifting provides the first step in a project to construct motives of rank 7 and weight 0 over Q with Galois group of type G(2).