Matt, Yemon, thank you very much, I've got it now. As far as reduced C* -algebra: is it functorial only for proper homomorphisms or condition of injectivity is sufficient? Thanks a lot.

Matt, thank you very much for your response! Your explanation of Q1 is great, I hope I understand all things maybe except one: could you explain how our * - homo l^1 (G)-> C*(H) defines a C*-norm on l^1(G)? As far as Q2, thank you, it is a good advice and we can provide a counterexample with a classical non - amenable group (free group of 2 generators) and free abelian group with 2 generators. Thank you very much one more time!

Thank you very much for your response! As far as my (and your) questions: Q1. I am interested in this question because I think that it is very natural but I can't find an explanation of this facts in the literature (I've read Davidson and Pedersen, for instance) Q2. Thank you very much for your hint, I understand it well now Q3. I know that C*(Z) = C(T), where T is unit circle, and C*(Z/nZ) = C^n.. As far as the nature of my interest - I am a low-dimensional topologist and I started to learn C* - algebras in connection with K-theory that could be useful in my science.