In my talk I will describe a particular case of the the global Langlands correspondence over function fields which valid for all split reductive groups. Our main result asserts that for every pair $(\pi,\omega)$, where $\pi$ is a cuspidal representation of $G$ one of whose local components is a stable cuspidal Deligne-Lusztig representation, and $\omega$ is a representation of the dual group, there exists a Galois representation $\rho_{\pi,\omega}$, whose $L$-function equals the $L$-function of the pair $(\pi,\omega)$. This is joint work in progress with David Kazhdan.