Suslin's conjecture on the image of the Hurewicz map

Let $F$ be an infinite field. The Quillen K-group is $K^Q_n(F)=\pi_n(BGL(F)^+)$, the Milnor K-group is $K^M_n(F)$, and Suslin's Hurewicz map is the natural map

$$K^Q_n(F)\longrightarrow K^M_n(F).$$

Suslin's conjecture. The image of Suslin's Hurewicz map coincides with

$$(n-1)!K^M_n(F).$$

Suslin's result that the composite $K^M_n(F)\longrightarrow K^Q_n(F)\longrightarrow K^M_n(F)$ is multiplication by $(-1)^n(n-1)!$ already shows that the image contains $(n-1)!K^M_n(F)$. The conjecture asserts that this evident containment is an equality for every infinite field.