the classifying space "bgl" is connected, so quillen's definition failed to give the correct value for "k". additionally, it did not give any negative "k"-groups. since "k" had a known and accepted definition it was possible to sidestep this difficulty, but it remained technically awkward. conceptually, the problem was that the definition sprung from "gl", which was classically the source of "k". because "gl" knows only about gluing vector bundles, not about the vector bundles themselves, it was impossible for it to describe "k".