Relative-partitioned index theorem
  It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and interesting examples of this program. In this paper we formulate a combination of these two theorems and establish a partitioned-relative index theorem. 
Moin Karami, Mostafa E. Zadeh, Ahmad H.S. Sadegh
math.KT