  We show that the Lagrangian for Lovelock-Cartan gravity theory can be
re-formulated as an action which leads to General Relativity in a certain
limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory
invariant under the generalized Poincar\'{e} algebra $\mathfrak{B}_{2n+1},$
while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant
under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that
torsion may occur explicitly in the Lagrangian leading to new torsional
Lagrangians, which are related to the Chern-Pontryagin character for the
$B_{2n+1}$ group.
