  A new approach to a unified theory of quantum gravity based on noncommutative
geometry and canonical quantum gravity is presented. The approach is built
around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold
and a quantized Dirac type operator; the two capturing the kinematics of
quantum gravity formulated in terms of Ashtekar variables. We prove that the
separable part of the spectrum of the algebra is contained in the space of
measurable connections modulo gauge transformations and we give limitations to
the non-separable part. The construction of the Dirac type operator -- and thus
the application of noncommutative geometry -- is motivated by the requirement
of diffeomorphism invariance. We conjecture that a semi-finite spectral triple,
which is invariant under volume-preserving diffeomorphisms, arise from a GNS
construction of a semi-classical state. Key elements of quantum field theory
emerge from the construction in a semi-classical limit, as does an almost
commutative algebra. Finally, we note that the spectrum of loop quantum gravity
emerges from a discretization of our construction. Certain convergence issues
are left unresolved. This paper is the first of two where the second paper is
concerned with mathematical details and proofs concerning the spectrum of the
holonomy-diffeomorphism algebra.
