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We construct an explicit example of a geometrically finite Kleinian group G with invariant component Ω in the Riemann sphere Ĉ such that any quasiconformal map from Ω to the boundary of the convex hull of Ĉ − Ω in H3 which extends to the identity map on their common boundary in Ĉ, and which is equivariant under the group of Möbius transformations preserving Ω, must have maximal dilatation K > 2.002.

An explicit counterexample to the equivariant 𝐾=2 conjecture