Matthias Kuenzer,
On representations of twisted group rings

Abstract.
We generalize certain parts of the theory of group rings to the twisted case. 
Let G be a finite group acting (possibly trivially) on a field L of 
characteristic coprime to the order of the kernel of this operation. Let 
K = L^G be the fixed field of this operation, let S be a discrete valuation 
ring with field of fractions K, maximal ideal generated by pi and integral 
closure T in L. We compute the colength of T~G in a maximal order in L~G. 
Moreover, if S/pi S is finite, we compute the S/pi S-dimension of the center 
of T~G/\Jac(T~G). If this quotient is split semisimple, this yields a formula 
for the number of simple T~G-modules, generalizing Brauer's formula.