Daniel Quillen gave a definition of the higher $K$-groups of a ring using $BGL(R)^+$ (The plus construction of classifying space of $R$), $K_n(R):= \pi_n(BGL(R)^+)$.Thus $BE(R)^+$ homotopic to universal cover of $BGL(R)^+$, then $K_n(R) \simeq \pi_n(BE(R)^+)$. Now I want to know how we construct $BE(R)^+$.
I would greatly appreciate it if you kindly give me some feedback on this question.