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• “A cocompletion theorem in K-theory for proper actions of adiscrete group”This refers to a paper joint with Michael Joachim [22] Let G be a discretegroup. We give methods to compute for a generalized (co-)homologytheory its values on the Borel construction EG × G X of a proper G-CW -complex X satisfying certain finiteness conditions. In particular wegive formulas computing the topological K-(co)homology K ∗ (BG) andK ∗ (BG) up to finite abelian torsion groups. They apply for instance toarithmetic groups, word hyperbolic groups, mapping class groups and discretecocompact subgroups of almost connected Lie groups. For finitegroups G these formulas are sharp. The main new tools we use for theK-theory calculation are a Cocompletion Theorem and Equivariant UniversalCoefficient Theorems which are of independent interest. In the casewhere G is a finite group these theorems reduce to well-known results ofGreenlees and Bökstedt. The cocompletion Theorem is obtained by dualizingthe equivariant version of the Atiyah-Segal completion theorem forproper actions of an infinite discrete group G in [62, 63].• “Waldhausen Additivity: Classical and Quasicategorical”Fiore and Lück [19] give a short proof of classical Waldhausen Additivity,and then prove Waldhausen Additivity for an ∞-version of WaldhausenK-theory. Namely, we prove that Waldhausen K-theory sends a splitexactsequence of Waldhausen quasicategories A → E → () to a stableequivalence of spectra K(E) → K(A) ∨ K(()) under a few mild hypotheses.For example, each cofiber sequence in A of the form A 0 → A 1 → ∗is required to have the first map an equivalence. Model structures, presentability,and stability are not needed. In an effort to make the articleself-contained, we provide many details in our proofs, recall all the prerequisitesfrom the theory of quasicategories, and prove some of those aswell. For instance, we develop the expected facts about (weak) adjunctionsbetween quasicategories and (weak) adjunctions between simplicialcategories.• “Equivariant principal bundles and their classifying spaces”In the paper [76] Uribe and I consider Γ-equivariant principal G-bundlesover proper Γ-CW -complexes with prescribed family of local representations.We construct and analyze their classifying spaces for locally compact,second countable topological groups with finite covering dimensionΓ and G such that G almost connected.14 Survey articlesWe mention the following survey articles: [15, 42, 43, 45, 46, 51, 53, 54,56, 57, 67].8