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We show that a pseudorepresentation $\textbf{D}\colon A[G] \to A$ of a(finite) group $G$ need not arise from a genuine representation, even if one isallowed to extend the ring $A$. This shows that a theorem of the "embeddingproblem" for residually multiplicity free pseudorepresentations can not beextended to the general setting.

Pseudorepresentations not arising from genuine representations