  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
$(k,\infty)$-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.
