  This paper determines tangential structure set of $\#_k\mathbb{C}P^{n}$, for
$3\leq n \leq 7$, by analyzing their stable cohomotopy groups and $KO$-groups.
As a consequence, it establishes the existence of manifolds with tangential
homotopy type but not homeomorphic to $\#_k\mathbb{C}P^{n}$ for $n=4,5$.
