On crossed product rings with twisted involutions, their module categories and L-theory

TL;DR

This paper extends the Farrell-Jones Conjecture to crossed product rings with twisted involutions, linking module categories and L-theory, and demonstrating broader applicability in algebraic K- and L-theory contexts.

Contribution

It introduces a variant of the L-theoretic Farrell-Jones Conjecture applicable to crossed product rings with twisted involutions, expanding the conjecture's scope.

Findings

The conjecture applies to crossed product rings with twisted involutions.

It implies the fibered version of the conjecture automatically.

The approach connects module categories with L-theory in new settings.

Abstract

We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show that this formulation of the conjecture can be applied to crossed product rings R*G equipped with twisted involutions and automatically implies the a priori more general fibered version.