Passage conjecture for L-theory from rational to real group rings and reduced real group C*-algebras

Let $G$ be a group, let $L_n^p$ denote the periodic $L$-groups, and let $j_2$ and $j_3$ be the maps in the diagram referenced in the source, comparing the rational and real group-ring terms with the reduced real group $C^*$-algebra term.

Passage conjecture. The maps $j_2$ and $j_3$ appearing in the diagram are bijective. The preceding discussion establishes several related comparison maps and split-injectivity results, while this particular passage statement is attributed to earlier questions in the cited literature and is not resolved in the supplied text.