On CAP automorphic representations of a split group of type D₄

We characterize a family of CAP (cuspidal representation associated to parabolic subgroup) automorphic representations of a split group G of type D₄ in terms of G₂-periods and Fourier coefficients attached to the subregular unipotent orbit of G. The existence of such CAP automorphic representations of G is proved by the theta correspondence using the exceptional automorphic theta functions on the split exceptional group of type E₇.