If I work over a field k,write D for the formal disk k[[t]] and D^x for the formal punctured disk k((t)), then there is an associated long exact sequence in algebraic K-theory

... K_n+1(D^x) --> K_n(k) --> K_n(D) --> K_n(D^x) ...

I want to know, what happens if we replace the base k by a more general scheme?

(I am particularly interested in the map K₂(D^x) --> K₁(k) (which must be the tame symbol right?))