Question

Is the fibered K-theoretic farrell-jones conjecture true for cat(0)-groups?

Answer 1

Yes. More precisely, both the L-theory and K-theory Farrell-Jones conjectures with coefficients in any additive category have recently been proved for CAT(0) groups:

• Arthur Bartels, Wolfgang Lück, “The Borel Conjecture for hyperbolic and CAT(0)-groups”, Annals of Mathematics 175 (2012), 631–689, http://dx.doi.org/10.4007/annals.2012.175.2.5
• Christian Wegner, “The K-theoretic Farrell-Jones conjecture for CAT(0)-groups”, http://arxiv.org/abs/1012.3349, to appear in Proceedings of the AMS.

In Arthur Bartels, Holger Reich, “Coefficients for the Farrell-Jones Conjecture”, Advances in Mathematics 209:1 (2007), 337–362, it is proved that “with coefficients is stronger than fibered,” see Corollary 4.3 and Remark 4.4 on page 346.

[Edited to clarify the relation between the “with coefficients” and “fibered” versions of the Farrell-Jones conjectures.]