Abstract
We introduce a twisted fiber bundle construction of quantum CSS codes over group algebras R=F₂[G], where each base generator carries a generator-dependent R-linear fiber twist satisfying a flatness condition. This construction extends the untwisted lifted product code, recovered when all twists are identities. We show that invertible twists (satisfying a flatness condition) give a complex chain-isomorphic to the untwisted one, so the resulting binary CSS codes have the same blocklength n and encoded dimension k. In contrast, singular chain-compatible twists can lower boundary ranks and increase the number of logical qubits. Examples over R=F₂[D₃] show that singular chain-compatible twists can increase the encoded dimension k at fixed blocklength n, and in these finite examples the minimum distance d remains unchanged. This provides evidence that singular twisting enlarges the design space beyond the ordinary lifted product construction.