Convolution morphisms and Kottwitz conjecture
We introduce convolution morphisms, duality morphisms and twist morphisms between moduli spaces of mixed characteristic local shtukas. Using these morphisms, we relate the etale cohomology of different moduli spaces of mixed characteristic local shtukas. As an application, we show the Kottwitz conjecture in many new cases including the cases for all inner forms of GL(3) and minuscule cocharacters. We study also some non-minuscule cases and show that the Kottwitz conjecture does not hold as it is in non-minuscule cases if the Langlands parameter is not cuspidal.