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 R2-theories of gravitation. Finally equivalence of the Lorentz gauge field theory coupled to spin zero matter with general relativity is established.