Let F be a function field and G a reductive group over F. We define a bilinear form B on the space of automorphic forms on G(A)/G(F) different from the standard inner product. For G = SL(2), the definition of B generalizes to the case where F is a number field (and this is expected to be true for any G). We discuss how B relates to pseudo-Eisenstein series and inversion of the standard intertwining operator. We show that this bilinear form is natural from the viewpoint of the geometric Langlands program via the functions-sheaves dictionary. We also give a formula for the operator on the space of automorphic forms corresponding to B. The inverse operator presents a global analog of the Aubert involution from the representation theory of p-adic groups.