  An integral kernel representation for the commutative $\star$-product on
curved classical spacetime is introduced. Its convergence conditions and
relationship to a Drin'feld differential twist are established. A
$\star$-Einstein field equation can be obtained, provided the matter-based
twist's vector generators are fixed to self-consistent values during the
variation in order to maintain $\star$-associativity. Variations not of this
type are non-viable as classical field theories. $\star$-Gauge theory on such a
spacetime can be developed using $\star$-Ehresmann connections. While the
theory preserves Lorentz invariance and background independence, the standard
ADM $3+1$ decomposition of 4-diffs in general relativity breaks down, leading
to different $\star$-constraints. No photon or graviton ghosts are found on
$\star$-Minkowski spacetime. $\star$-Friedmann equations are derived and solved
for $\star$-FLRW cosmologies. Big Bang Nucleosynthesis restricts expressions
for the twist generators. Allowed generators can be constructed which account
for dark matter as arising from a twist producing non-standard model matter
field. The theory also provides a robust qualitative explanation for the
matter-antimatter asymmetry of the observable Universe. Particle exchange
quantum statistics encounters \emph{thresholded} modifications due to
violations of the cluster decomposition principle on the nonlocality length
scale $\sim10^{3-5} \,L_P$. Precision Hughes-Drever measurements of spacetime
anisotropy appear as the most promising experimental route to test deformed
general relativity.
