  For our own education, we reconstruct the Hopf algebra of Connes and
Moscovici obtained by the action of vector fields on a crossed product of
functions by diffeomorphisms. We extend the realization of that Hopf algebra in
terms of rooted trees as given by Connes and Kreimer from dimension one to
arbitrary dimension of the manifold. In principle there is no modification, but
in higher dimension one has to be careful with the order of cuts. The order
problem leads us to speculate that in quantum field theory the sum of Feynman
graphs which corresponds to an element of the Connes-Moscovici Hopf algebra
could have a larger symmetry than the individual graphs.
