  A gauge theory of the Lorentz group with a mass-dimension one gauge field
coupling to matter of any spin is developed. As a completely new feature the
"Vierbein" assuring local gauge invariance enters not as an independent
dynamical field, but emerges as a functional of the Lorentz gauge field. The
underlying geometry of the theory turns out to be a $SO(1,3)$ Banach bundle.
The most general action which is renormalizable by power-counting is
constructed in terms of the gauge field and its first derivatives. It contains
no higher derivative terms in the gauge field which destroy unitarity in the
usual renormalizable $R^2$-theories of gravitation. Finally equivalence of the
Lorentz gauge field theory coupled to spin zero matter with General Relativity
is established
