What is an awesome C*-algebras result and/or theory derived from C*-algebra Theory First of all, I'm deeply sorry this isn't a real math. question, but 'meta' didn't seem like the right place to ask this either.
So there goes: 
I'm studying representation theory and operator theory for my master's thesis and found out about this cool theory, $C^*$-algebras and read it has a central role in representation theory of general vector spaces, and other algebraic structures. 
Now what I need is an interesting result about this theory to reach in this thesis. Deep, recent, hard, sophisticated or not... Even if it's an application of the theory to another area.
Hope the mods won't be mad about this.
Any help will be appreciated.
Thanks in advance. 
HTTT.
 A: Sorry I'm a little late but here are some. Note: Though I am an operator algebraist, I'm not a $C^*$-algebraist. Also (from my understanding) $C^*$-algebras are not as useful in representation theory as say some of the founders of the theory had desired. So much of this will be purely for operator algebra interests though there is some applications. Finally I'm not quite sure what level you want (is this for a master's thesis?). But enough with the preliminaries...
1.) K-theory. This is a quite large area (here I include K-homology and the bivariant KK-theory) including BDF theory and much of the classical topological K-theory. In fact there is a reasonably short proof of Bott periodicity by Cuntz (this is suitable for an undergrad honor thesis, it was mine). Going on from this you can go onto to classify approximatly finite dimensional algebras.
2.) Related to the first there is the theory of nuclear $C^*$-algebras. This could include, Haagerup's characterization as amenable $C^*$-algebras as well as Eliot's classification theory.
3.) Non-commutative geometry. This is a HUGE area (in fact it subsumes 1) but specifically things which I think are particularly nice are the Baum-Connes conjecture related things. In particular the proof of Baum-Connes for groups with the Haagerup property (I haven't looked at this so am not sure if this at an appropriate level). There is also the related work on the strong Novikov conjecture. 
4.) Kirchberg's work on exact $C^*$-algebras.
5.) Ozawa work on solid von Neumann algebras uses significant amount of $C^*$-algebra theory (though these methods have been subsumed by now by other methods).
These are just a few. I can give some references if you would like, I know this is alot to take in. 
