  We derive an interacting quintessence model on the framework of a recently
introduced new class of geometrical scalar-tensor theories of gravity
formulated on a Weyl-Integrable geometry, where the gravitational sector is
described by both a scalar and a tensor metric field. By using a Palatini
variational principle we construct a scalar-tensor action invariant under the
Weyl symmetry group of the background geometry, which in the Einstein-Riemann
frame leads to a gravitoelectromagnetic theory. We use the gauge freedom of the
theory and the fact that the Weyl scalar field couples with matter fields to
formulate an interacting quintessential model with a non-canonical kinetic
term, where the quintessence field has a geometrical origin. Due to this
non-canonicity we obtain that the mass of the quintessence field in the past
epochs results to be small enough not to cause modifications in the baryon to
photon ratio during nucleosynthesis.
