We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes–Moscovici cyclic cocycle for the Godbillon–Vey secondary characteristic class.
"The Godbillon–Vey invariant and equivariant $KK$-theory." Ann. K-Theory 5 (2) 249 - 294, 2020. https://doi.org/10.2140/akt.2020.5.249