An admissible subcategory $C\subset D$ of a triangulated category is called phantom if $K_0(C)=0$. Such categories may be detected by their Hochschild cohomology (but usually have trivial Hochschild homology). Is there an example of phantom category with trivial Hochschild cohomology?

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    $\begingroup$ An admissible subcategory has trivial Hochschild cohomology iff it is trivial: consider the identity map! $\endgroup$ – naf May 19 '17 at 5:03

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