Interior Kasparov products for (SIC)-classes on Riemannian foliated bundles

Let t: F0-+ F1 be a suitably oriented inclusion of foliations over a manifold M, then we extend the construction of the lower shriek maps given by Hilsum and Skandalis to adiabatic deformation groupoid C*-algebras: we construct an ( ) asymptotic morphism (t[0,1) ad )! E En C*(G[0,1) ad),C*(G[0,1) ad ) , where G and H are the monodromy groupoids associated with F0 and F1 respectively. Furthermore, we prove an interior Kasparov product formula for foliated p -classes associated with longitudinal metrics of positive scalar curvature in the case of Riemannian foliated bundles. (c) 2023 Elsevier Inc. All rights reserved.