I have seen it the claimed that the Einstein-Hilbert action can be written in terms of a tetrad ##e_{\mu} \, ^a## as
\begin{align}
S &= \int d^n x \, e R(e_{\mu} \, ^a, \omega_{\mu a} \, ^b (e)) \\
&= \int d^n x \, e (T_{ca} \, ^a T^{cb} \, _{b} - \frac{1}{2} T_{ab \ c} T^{ac \ b} -...