  The K-theoretic Farrell-Jones isomorphism conjecture for a group ring $R[G]$
has been proved for several groups. The toolbox for proving the Farrell-Jones
conjecture for a given group depends on some geometric properties of the group
as it is the case of hyperbolic groups. The technique used to prove it for
hyperbolic groups $G$ relies in the concept of an $N$-transfer space endowed
with a $G$ action. In this work, we give an explicit construction of a
$1$-transfer space.
