I am working on Fabien Morel's paper : "A1-Algebraic topology over a field" and I am a bit confused about certains properties of classifying spaces.
For example : How to show that $BSL_r \longrightarrow BGL_r$ is a $G_m$-torsor?
Here $BGL_r$ and $BSL_r$ are living in the $A^1$-homotopy category of schemes over a field.