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Let L S (π, s, st) be a partial L-function of degree 7 of a cuspidal automorphic representation π of the exceptional group G 2 . Here we construct a Rankin-Selberg integral for representations having certain Fourier coefficient.

We give a construction of a family of CAP representations of the exceptional group G 2 , whose existence is predicted by Arthur's conjecture. These are constructed by lifting certain cuspidal representations of P GSp 6 . To show that the lifting is non-zero, we establish a Rankin-Selberg integral for the degree 8 Spin L-function of these cuspidal representations of P GSp 6 .

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