We prove the Farrell–Jones conjecture for algebraic -theory of spaces for virtually poly--groups. For this, we transfer the “Farrell–Hsiang method” from the linear case to categories of equivariant, controlled retractive spaces.
"On the Farrell–Jones conjecture for algebraic $K$-theory of spaces: the Farrell–Hsiang method." Ann. K-Theory 4 (1) 57 - 138, 2019. https://doi.org/10.2140/akt.2019.4.57