K_2 of rings of algebraic integers Let $R$ be the ring of integers in an algebraic number field.  There are beautiful descriptions of $K_0(R)$ and $K_1(R)$.  Namely, $\tilde{K}_0(R)$ is the class group of $R$ and $K_1(R)$ is the group of units of $R$.  Question : Is there a nice description of $K_2(R)$ (or at least some reasonable conjectures)?  I couldn't find much about this in Milnor's or Rosenberg's books on algebraic K-theory, so I expect that the answer is pretty complicated.  Is it maybe at least known in some special cases (say, for $R$ the integers in a quadratic extension of $\mathbb{Q}$)?
 A: $K_1$ being the units, and Dirichlet's theorem on the unit group, generalize to odd K-groups via regulator maps and related conjectures and theorems (starting from work of Borel, Bloch, Beilinson, Zagier, and many others).  For the even K-groups I don't know of any such description.
Charles Weibel's web page has a K-theory textbook with a chapter on $K_1$ and $K_2$, and a paper on the early history of K-theory.  Both of those discuss $K_2$ of rings of integers in a number field, but I didn't see any characterization analogous to the one with regulators for $K_1$ or $K_3$.
I'm certainly not an expert on this subject but I have the feeling that if a snazzy description of $K_2({O_F})$ were proven or conjectured, it would be widely known.
A: I think Kolster's survey is a good introduction to questions related to 
arithmetic interpretations of higher K-groups.
A: I've never heard of $K_2(R)$ having a description as a more easily/elementarily described object attached to $R$. Borel showed that $K_2(R)$ is torsion. The order of $K_2(R)$ appears in "Theorem" 31 of Soulé's notes on higher algebraic K-theory of rings of algebraic integers where $K_2(R)$ (I think that "Theorem" 31 is called the Quillen-Lichtenbaum conjecture).
A: For the conjectural order, see the Birch-Tate conjecture http://eom.springer.de/B/b110560.htm .
A: It's a theorem of Garland that $K_2(R)$ is finite. Perhaps the best way to get a handle on it is to use Quillen's localization sequence
$$0\rightarrow K_2(R)\rightarrow K_2(F)\stackrel{T}{\rightarrow} \oplus_v k(v)^*\rightarrow 0,$$
where $F$ is the fraction field and the $k(v)$ are the residue fields. The map $T$ is the sum of the tame symbols, which is surjective by a theorem of Matsumoto. The injectivity on the left follows from the vanishing of $K_2$ for finite fields. 
This isn't much of an answer, but considering $K_2(R)$ as a subgroup of $K_2(F)$ seems a reasonable way to start some concrete considerations. For a detailed discussion of an algorithm  that proceeds essentially along these lines ('Tate's method), see the paper 
Belabas, Karim; Gangl, Herbert
Generators and relations for $K_2( O_F)$. 
$K$-Theory 31 (2004), no. 3, 195--231.
Added, 8 July:
I'm sure most people know this, but I forgot to mention (for newcomers) the fact that
$$K_2(F) = F^\times\otimes_{\mathbf Z} F^\times/\langle a\otimes(1-a)\mid a\not=0,1\rangle,$$
which I suppose motivates the original question, and makes it worthwhile to view $K_2(R)$ as a subgroup.
