Let G be a connected reductive group G over a finite field with dual group G*, and consider a morphism r from G* to GL(n). From the standard Fourier transform on GL(n) and the morphism r, Braverman and Kazhdan defined an exotic Fourier operator on the space of functions on G(q) using Langlands functoriality. They also gave a conjectural formula for its kernel. In this talk we will give a proof of their conjecture. This is joint work with Grard Laumon.