By work of Kato, Venjakob, and others, the Iwasawa-theoretic concept of a characteristic power series requires the passage to a very specific localization of an Iwasawa algebra. In the p-adic representation theory of p-adic reductive groups Iwasawa algebras appear disguised as distribution algebras. More surprisingly, recent developments in the search for a p-adic local Langlands program indicate that the p-adic completion of the very same localization (in the case of a unipotent group) will play an important role. It allows to set up a higher dimensional (and noncommutative) analog of Fontaine's theory of (phi,Gamma)-modules. In joint work with Venjakob we have constructed these completions explicitly as rings of skew Laurent series.

I will mostly give a general survey of these developments. Towards the end I will try to entertain the audience with some explicit formulas showing how to multiply skew Laurent series.