The Full Farrell–Jones conjecture

Let $G$ and $F$ be groups, and define their wreath product by $G\wr F=(\prod_F G)\rtimes F$, with $F$ permuting the factors. The Full Farrell–Jones conjecture. A group $G$ satisfies the Full Farrell–Jones conjecture if, for every finite group $F$, the wreath product $G\wr F$ satisfies the K-theoretic Farrell–Jones conjecture with additive $G$-category coefficients, the L-theoretic Farrell–Jones conjecture with additive $G$-category coefficients with involution, and the K-theoretic Farrell–Jones conjecture with higher $G$-category coefficients. This formulation packages the three coefficient versions and is intended to capture the full Farrell–Jones property; the source gives no resolution status.