  The monoids l_{2q+1}(Z[\pi]) detect s-cobordisms amongst certain bordisms
between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall
simple surgery obstruction groups, L_{2q+1}^s(Z[\pi]) \subset l_{2q+1}(Z[\pi]).
In this paper we give exact sequences which completely describe
l_{2q+1}(Z[\pi]) as a set and which we use to compute its Grothendieck group.
As a consequence we deduce cancellation results for stably diffeomorphic
manifolds with polycyclic-by-finite fundamental group.
