  In this paper, we present the idea that the formalism of string theory is
connected with the dimension 4 in a new way, not covered by phenomenological or
model-building approaches. The main connection is given by structures induced
by small exotic smooth R^4's having intrinsic meaning for physics in dimension
4. We extend the notion of stable quantum D-branes in a separable
noncommutative C* algebras over convolution algebras corresponding to the
codimension-1 foliations of S^3 which are mainly connected to small exotic R^4.
The tools of topological K-homology and K-theory as well KK-theory describe
stable quantum branes in the C* algebras when naturally extended to algebras.
In case of convolution algebras, small exotic smooth R^4's embedded in exotic
R^4 correspond to a generalized quantum branes on the algebras. These results
extend the correspondence between exotic R^4 and classical D and NS branes from
our previous work.
