The Lefschetz homomorphism from endotrivial complexes to orthogonal units of the trivial source ring is surjective for several families of finite groups (2-fusion controlled or dihedral Sylow 2-subgroups for p=2; cyclic Sylow or p-nilpotent for odd p), but not surjective for some groups of p-rank at
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The Euler characteristic of an endotrivial complex
The Lefschetz homomorphism from endotrivial complexes to orthogonal units of the trivial source ring is surjective for several families of finite groups (2-fusion controlled or dihedral Sylow 2-subgroups for p=2; cyclic Sylow or p-nilpotent for odd p), but not surjective for some groups of p-rank at