In these two talks I will present my current project on endowing a torsor structure on L-packet of the covering tori. In the first half I will talk about how to construct gerbes on the groupoid of isocrystals, and a formulation of the Langlands correspondence of sharp covering tori on the level of gerbes. In the second half I will talk about how the groupoid of isocrystals of the sharp tori can help to interpolate the L-packets of different extended pure inner forms of the covering tori, which gives rise to the desired torsor structure.