  We study algebraicity and smoothness of fixed point stacks for flat group
schemes which have a finite composition series whose factors are either
reductive or proper, flat, finitely presented, acting on algebraic stacks with
affine, finitely presented diagonal. For this, we extend some theorems of
[SGA3.2] on functors of homomorphisms Hom(G, H) and functors of reductive
subgroups Sub(H) for an affine, possibly non-flat group scheme H.
