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Let $E/F$ be a quadratic extension of fields, and $G$ a connected quasi-splitreductive group over $F$. Let $G^{op}$ be the opposition group obtained bytwisting $G$ by the duality involution considered by Prasad. Assume that thefield $F$ is finite. Let $\pi$ be an irreducible generic representation of$G(E)$. When $\pi$ is a Shintani base change lift of some representation of$G^{op}(F)$, we give an explicit nonzero $G(F)$-invariant vector in terms ofthe Whittaker vector of $\pi$. This shows particularly that $\pi$ is$G(F)$-distinguished.  When the field $F$ is $p$-adic, the paper also proves that the dualityinvolution takes an irreducible admissible generic representation of $G(F)$ toits contragredient. As a special case of this result, all genericrepresentations of $G_2,\ F_4$ or $E_8$ are self-dual.

Distinguished representations, Shintani base change and a finite field analogue of a conjecture of Prasad