  Recent work on exotic smooth R^4's, i.e. topological R^4 with exotic
differential structure, shows the connection of 4-exotics with the
codimension-1 foliations of $S^{3}$, SU(2) WZW models and twisted K-theory
$K_{H}(S^{3})$, $H\in H^{3}(S^{3},\mathbb{Z})$. These results made it possible
to explicate some physical effects of exotic 4-smoothness. Here we present a
relation between exotic smooth R^4 and operator algebras. The correspondence
uses the leaf space of the codimension-1 foliation of S^3 inducing a von
Neumann algebra $W(S^{3})$ as description. This algebra is a type III_1 factor
lying at the heart of any observable algebra of QFT. By using the relation to
factor II, we showed that the algebra $W(S^{3})$ can be interpreted as
Drinfeld-Turaev deformation quantization of the space of flat SL(2,\mathbb{C})
connections (or holonomies). Thus, we obtain a natural relation to quantum
field theory. Finally we discuss the appearance of concrete action functionals
for fermions or gauge fields and its connection to quantum-field-theoretical
models like the Tree QFT of Rivasseau.
