The Hsiang conjecture on rationalized classical assembly

Let $G$ be a torsion-free group and $n\in\mathbb{Z}$. The rationalized classical assembly map is

$$\bigoplus_{\substack{s+t=n\s,t\geq0}} H_s(BG;\mathbb{Q})\otimes_{\mathbb{Q}}\bigl(K_t(\mathbb{Z})\otimes_{\mathbb{Z}}\mathbb{Q}\bigr)\longrightarrow K_n(\mathbb{Z}G)\otimes_{\mathbb{Z}}\mathbb{Q}.$$

Hsiang's conjecture. For every torsion-free group $G$ and every $n\in\mathbb{Z}$, this rationalized classical assembly map is an isomorphism.

The conjecture was formulated by Hsiang in his 1983 ICM plenary address, originally under an additional finite-classifying-space hypothesis. It is a rational form of the torsion-free assembly conjecture.