A K-theory spectrum for cobordism cut andpaste groups

Cobordism groups and cut and paste groups of manifolds arise from imposing two different relations on the monoid of manifolds under disjoint union.By imposing both relations simultaneously, a cobordism cut and paste group SK n is defined.We extend this definition to manifolds with boundary, obtaining the group SK @ n , and study the relationship of the group to an appropriately defined cobordism group of manifolds with boundary.The main results are the construction of a spectrum that recovers on 0 the cobordism cut and paste groups of manifolds with boundary, SK @ n , and a map of spectra that lifts the canonical quotient map SK @