  This paper deals with certain results on the number of smooth structures on
quaternionic projective spaces, obtained through the computation of inertia
group and its analogues, which in turn are computed using techniques from
stable homotopy theory. We show that the concordance inertia group is trivial
in dimension 20, but there are many examples in high dimensions where the
concordance inertia group is non-trivial. We extend these to computations of
concordance classes of smooth structures. These have applications to 3-sphere
actions on homotopy spheres and tangential homotopy structures.
