TITLE: Can anyone explain to me what is an assembly map?
QUESTION [16 upvotes]: Or can you give me a good place to read about things related to assembly map, besides wikipedia? I am specially interested in the case of algebraic K-theory. Would appreciated if you could provide examples.

REPLY [3 votes]: You can find lots of definitions in Hambleton and Pedersen's paper "Identifying assembly maps in K- and L-theory " at http://www.maths.ed.ac.uk/~aar/papers/idensurg.pdf
For a torsion-free group $G$, the assembly map $H_n(BG;K\mathbb{Z})\rightarrow K_n(\mathbb{Z}G))$ is induced by the contraction $EG\rightarrow pt$. In General, the algebraic $K$-theory is difficult to compute. The Farrell-Jones conjecture (claiming the assembly map is an isomorphism for each $n$) says that the algebraic $K$-theory of group rings can be computed by a homology theory, which is easier to deal with.