The Quillen plus construction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groups. It was introduced by Kervaire (1969), but was crucially used by Daniel Quillen to define the algebraic K-theory groups by applying it to the classifying space of the stable general linear group, , of a ring .
The plus construction doesn’t change the homology of the space but ‘kills’ a perfect normal subgroup of within the classifying space . For algebraic K-theory, that subgroup is the stable elementary linear group?, within .
See section IV.1 of