In this paper we define new K-theoretic secondary invariants attached to a Lie groupoid G. The receptacle for these invariants is the K-theory of Cr⁎(Gad∘) (where Gad∘ is the adiabatic deformation G restricted to the interval 0,1)). Our construction directly generalises the cases treated in 29,30, in the setting of the Coarse Geometry, to more involved geometrical situations, such as foliations. Moreover we tackle the problem of producing a wrong-way functoriality between adiabatic deformation groupoid K-groups associated to transverse maps. This extends the construction of the lower shriek map in 6. Furthermore we prove a Lie groupoid version of the Delocalized APS Index Theorem of Piazza and Schick. Finally we give a product formula for secondary invariants.