This talk aims to give an exposition of recent work of Ash-Miller-Patzt, establishing a Hopf algebra structure on the cohomology groups H^k(GLnZ; Q). These groups are of interest in several areas of mathematics, including K-theory of the integers and automorphisms of free groups, but have proven difficult to compute. I will discuss how they can be studied via "Steinberg modules", describe how this can be used to put a Hopf algebra structure on them, and how this helps to find new cohomology classes.