The Langlands-Rapoport Conjecture for global G-Shtukas

The conjecture of Langlands and Rapoport gives a group theoretic description of the points on a Shimura variety with values in a finite field. The function field analog of Shimura varieties are moduli stacks of global $G$-shtukas. We will formulate the function field analog of the Langlands-Rapoport conjecture for the latter moduli stacks and prove it in certain cases.