  The field equations of general relativity can be derived from the Einstein
action, which is quadratic in connection coefficients, rather than the standard
action involving the Gibbons-Hawking-York term and counterterm. We show that it
is possible to construct a new counterterm directly for the Einstein action,
which removes divergences and naturally introduces a flat reference spacetime.
The total action is then covariant under simultaneous transformation of both
the spacetime and reference tetrads, and argue that this is analogous to the
Gibbons-Hawking action. We then explore different perspectives arising
naturally from different uses of the reference tetrad, and explore implications
of viewing gravity as fundamentally described in terms of non-covariant
connection coefficients.
