This paper is comprised of two related parts. First we discuss which k-graph
algebras have faithful gauge invariant traces, where the gauge action of T^k is the canonical
one. We give a sufficient condition for the existence of such a trace, identify the C*-algebras of
k-graphs satisfying this condition up to Morita equivalence, and compute their K-theory.
For k-graphs with faithful gauge invariant trace, we construct a smooth (k,infinity)-summable
semifinite spectral triple. We use the semifinite local index theorem to compute the pairing
with K-theory. This numerical pairing can be obtained by applying the trace to a KK-pairing
with values in the K-theory of the fixed point algebra of the T^k action. As with graph algebras,
the index pairing is an invariant for a finer structure than the isomorphism class of the algebra.