The fusion algebra of the Wess–Zumino–Witten conformal field theory corresponding to a compact connected simply connected Lie group was identified by D. S. Freed, M. J. Hopkins and C. Teleman [J. Topol. 1, No. 1, 16–44 (2008; Zbl 1188.19005)] with the twisted equivariant \(K\)-theory. The authors study how to recover the full system (fusion algebra of defect lines), nimrep (cylindrical partition function), etc. of modular invariant partition functions of conformal field theories associated to loop groups. They work out several examples corresponding to conformal embeddings and orbifolds. A new aspect of the A-D-E pattern of \(\text{SU}(2)\) modular invariants is identified.