In this talk, I will introduce a simple technique for lifting a bounded linear operator with finite propagation on a metric space (specifically, a Riemannian manifold) to its covering space. This lifting induces a homomorphism between operator algebra K-groups, which non-trivially relates an index-theoretic invariant to another. This answers some questions in both differential topology (Schick's meta-conjecture on positive scalar curvature metric) and condensed matter physics (the bulk-dislocation correspondence).