  Exotic spinor fields arise from inequivalent spin structures on non-trivial
topological manifolds, $M$. This induces an additional term in the Dirac
operator, defined by the cohomology group $H^1(M,\mathbb{Z}_2)$ that rules a
Cech cohomology class. This formalism is extended for manifolds of any finite
dimension, endowed with a metric of arbitrary signature. The exotic corrections
to heat kernel coefficients, relating spectral properties of exotic Dirac
operators to the geometric invariants of $M$, are derived and scrutinized.
