  By using the relation between foliations and exotic R^4, orbifold $K$-theory
deformed by a gerbe can be interpreted as coming from the change in the
smoothness of R^4. We give various interpretations of integral 3-rd cohomology
classes on S^3 and discuss the difference between large and small exotic R^4.
Then we show that $K$-theories deformed by gerbes of the Leray orbifold of S^3
are in one-to-one correspondence with some exotic smooth R^4's. The equivalence
can be understood in the sense that stable isomorphisms classes of bundle
gerbes on S^{3} whose codimension-1 foliations generates the foliations of the
boundary of the Akbulut cork, correspond uniquely to these exotic R^{4}'s.
Given the orbifold $SU(2)\times SU(2)\rightrightarrows SU(2)$ where SU(2) acts
on itself by conjugation, the deformations of the equivariant $K$-theory on
this orbifold by the elements of $H_{SU(2)}^{3}(SU(2),\mathbb{Z})$, correspond
to the changes of suitable exotic smooth structures on R^4.
