2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224835We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery which produces equivariant generalized homology theories from such simple and abundant data as partial monoids.This is the version published by Geometry & Topology Monographs on 18 April 2007Algebraic Topology55N20, 55N91, 55P47text