  This contribution is the first in a series of three: it reports on the
construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras
on open sets of Eucildean space, which completes earlier approaches. Part II
and III will show, among others, the way to an intrinsic definition of
Colombeau algebras on manifolds which, locally, reproduces the local
diffeomorphism invariant theory.
