  In a spatially flat \ Friedmann--Lema\^{\i}tre--Robertson--Walker background
space we consider a scalar-torsion gravitational model which has similar
properties with the dilaton theory. This teleparallel model is invariant under
a discrete transformation similar to the Gasperini-Veneziano duality
transformation. Moreover, in the gravitational Action integral we introduce the
Lagrangian function of a pressureless fluid source which is coupled to the
teleparallel dilaton field. This specific gravitational theory with interaction
in the dark sector of the universe is investigated by using methods of the
dynamical system analysis. We calculate that the theory provides various areas
of special interest for the evolution of the cosmological history. Inflationary
scaling solutions and the de Sitter universe is recovered. Furthermore, we
calculate that there exist an attractor which provides a stable solution where
the two fluid components, the scalar field and the pressureless matter,
contribute in the cosmological fluid. This solution is of special interest
because it can describe the present epoch. Finally, the qualitative evolution
of the cosmographic parameters is discussed.
