Limit Sets for Modules over Groups Acting on a CAT(0) Space

This is a summary, written by the first-named author, of my joint work with Ross Geoghegan over the past years. Most of the material is available in detail in [4], and I will occasionally refer to specific detail in that paper. Other parts of our joint work - results mostly concerned with extending concepts and results from [4] to higher dimensions - will also be mentioned but are still in preparation. I am very pleased for this opportunity to thank my friend Ross for his excellent, enjoyable and fruitful collaboration over more than 15 years. Obviously, I cannot dedicate this joint summary to him ... but do it with what I found in the process of writing: I dedicate to Ross the conjectures in Section 3.5 on the occasion of his 70th birthday (while at the same time keeping the responsibility for their accuracy).