We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that $A{\otimes }_{min}B$ inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove that G/Γ is...