  The bulk-boundary and a new bulk-defect correspondence principles are
formulated using groupoid algebras. The new strategy relies on the observation
that the groupoids of lattices with boundaries or defects display spaces of
units with invariant accumulation manifolds, hence they can be naturally split
into disjoint unions of open and closed invariant sub-sets. This leads to
standard exact sequences of groupoid $C^\ast$-algebras that can be used to
associate a Kasparov element to a lattice defect and to formulate an extremely
general bulk-defect correspondence principle. As an application, we establish a
correspondence between topological defects of a 2-dimensional square lattice
and Kasparov's group $KK^1 (C^\ast(\mathbb Z^3),\mathbb C)$. Numerical examples
of non-trivial bulk-defect correspondences are supplied.
