  The dark matter and dark energy problem, that is now dominating the research
in cosmology, makes the question of the origin of mass-energy content of the
universe more urgent than ever. There are two philosophies regarding this
question: according to Mach's principle it is matter that generates geometry of
space-time, and according to Wheeler's geometrodynamics some configurations of
space-time geometry are to be interpreted as its material content. Neither of
these philosophies has led to success. In the present paper, we show that there
exists an algebraic generalisation of geometry that reconciles, in a sense,
these two seemingly opposite standpoints. The geometry is constructed with the
help of a noncommutative algebra of smooth functions on a groupoid and its
derivations. The groupoid in question has a nice physical interpretation: it
can be regarded as a space of Lorentz rotations. In this way, Lorentz
symmetries are inherent to the generalised geometry of space-time. We define
the action for this geometry and, by varying it, obtain generalised vacuum
Einstein equations (for a simplified model). It turns out that these equations
contain additional terms (with respect to the standard vacuum Einstein
equations) which are naturally interpreted as the components of the
energy-momentum tensor. Matter is thus created out of purely geometric degrees
of freedom. We find two exact solutions (for even more simplified case). We
argue that the creation of matter, being a global effect, makes the contrast
between Mach and Wheeler philosophies ineffective.
