  We review the first order theory of gravity (vierbein formulation) on
noncommutative spacetime studied in [1, 2]. The first order formalism allows to
couple the theory to fermions. This NC action is then reinterpreted (using the
Seiberg-Witten map) as a gravity theory on commutative spacetime that contains
terms with higher derivatives and higher powers of the curvature and depend on
the noncommutativity parameter \theta. When the noncommutativity is switched
off we recover the usual gravity action coupled to fermions. The first
nontrival corrections to the usual gravity action coupled to fermions are
presented in a manifest Lorentz invariant form.
