 
Summary: Z .Journal of Algebra 217, 249 274 1999
Article ID jabr.1998.7783, available online at http:rrwww.idealibrary.com on
Projective Representations and Relative Semisimplicity
E. Aljadeff and U. Onn
Department of Mathematics, Technion, Haifa 32000, Israel
and
Y. Ginosar
Department of Mathematics, Brandeis Unišersity, Waltham, Massachusetts 022549110
Communicated by D. A. Buchsbaum
Received March 27, 1998
DEDICATED TO DEREK J. S. ROBINSON ON THE OCCASION
OF HIS 60TH BIRTHDAY
Z .Let R be a local commutative ring and let p be a prime not invertible in R.
Let G be a finite group of order divisible by p. It is well known that the group ring
Z .RG admits nonprojective lattices e.g., R itself with the trivial action . For any
2Z .element g H G, R* one can form the twisted group ring R G. The ``twisting
problem'' asks whether there exists a class s.t. the corresponding twisted group
ring admits only projective lattices. For fields of characteristic p, the answer is in
w Z . xE. Aljadeff and D. J. S. Robinson J. Pure Appl. Algebra 94 1994 , 1 15 . Here we
answer this question for rings of the form s, s G 2. The main tools are thep
