  Since the first work on exotic smoothness in physics, it was folklore to
assume a direct influence of exotic smoothness to quantum gravity. Thus, the
negative result of Duston (arXiv:0911.4068) was a surprise. A closer look into
the semi-classical approach uncovered the implicit assumption of a close
connection between geometry and smoothness structure. But both structures,
geometry and smoothness, are independent of each other. In this paper we
calculate the "smoothness structure" part of the path integral in quantum
gravity assuming that the "sum over geometries" is already given. For that
purpose we use the knot surgery of Fintushel and Stern applied to the class
E(n) of elliptic surfaces. We mainly focus our attention to the K3 surfaces
E(2). Then we assume that every exotic smoothness structure of the K3 surface
can be generated by knot or link surgery a la Fintushel and Stern. The results
are applied to the calculation of expectation values. Here we discuss the two
observables, volume and Wilson loop, for the construction of an exotic
4-manifold using the knot $5_{2}$ and the Whitehead link $Wh$. By using Mostow
rigidity, we obtain a topological contribution to the expectation value of the
volume. Furthermore we obtain a justification of area quantization.
