In gauge theories parallel transporters (PTs) \documentclass[12pt]{minimal}
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\begin{document}$\mathcal{U}(C)$\end{document} along paths C play an important role. Traditionally they are unitary or pseudoorthogonal maps between vector spaces. We propose to abandon unitarity of parallel transporters and with it the a priori assumption of metricity in general relativity. A *-operation on parallel transporters serves as a substitute for it, and this *-operation is proven to be unique on group theoretical grounds. The vierbein and the spin connection appear as distinguishable parts of a single de Sitter gauge field with field strength F. The action takes the form \documentclass[12pt]{minimal}
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\begin{document}$\frac{3}{16\pi G\Lambda}\int\text{tr}(\boldsymbol{F}\wedge\boldsymbol{F}i\boldsymbol{\gamma}_{5})$\end{document} and both the Einstein field equations with arbitrarily small but nonvanishing cosmological constant Λ and the condition of vanishing torsion are obtained from it. The equation of motion for classical massive bodies turns out to be de Sitter covariant.
