We show that if M and N have the same homotopy type of simply connected closed smooth m-manifolds such that the integral and mod-2 cohomologies of M vanish in odd degrees, then their homotopy inertia groups are equal. Let  be a closed -connected 2n-dimensional smooth manifold. We show that, for  the homotopy inertia group of  is trivial and if  and  then the homotopy inertia group of  is also trivial. We further compute the group  of concordance classes of smoothings of  for  Finally, we show that if a smooth manifold N is tangentially homotopy equivalent to  then N is diffeomorphic to the connected sum of  and a homotopy 8-sphere.

projective plane like manifolds, smooth structures, homotopy inertia groups, cohomotopy groups.