On the Morita Frobenius numbers of blocks of finite reductive groups

We show that the Morita Frobenius number of the blocks of the alternating groups, the finite groups of Lie type in defining characteristic, and the Ree and Suzuki groups is 1. We also show that the Morita Frobenius number of almost all of the unipotent blocks of the finite groups of Lie type in non-defining characteristic is 1, and that in the remaining cases it is at most 2.