  We show how to get a non-commutative product for functions on space-time
starting from the deformation of the coproduct of the Poincare' group using the
Drinfel'd twist. Thus it is easy to see that the commutative algebra of
functions on space-time (R^4) can be identified as the set of functions on the
Poincare' group invariant under the right action of the Lorentz group provided
we use the standard coproduct for the Poincare' group. We obtain our results
for the noncommutative Moyal plane by generalizing this result to the case of
the twisted coproduct. This extension is not trivial and involves cohomological
features. As is known, spacetime algebra fixes the coproduct on the
dffeomorphism group of the manifold. We now see that the influence is
reciprocal: they are strongly tied.
