  It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted
group algebras in a pointed fusion category serve as explicit Morita
equivalence class representatives of indecomposable, separable algebras in such
categories. We generalize this result by constructing explicit Morita
equivalence class representatives of indecomposable, separable algebras in
group-theoretical fusion categories. This is achieved by providing the free
functor $\Phi$ from fusion category to a category of bimodules in the original
category with a (Frobenius) monoidal structure. Our algebras of interest are
then constructed as the image of twisted group algebras under $\Phi$. We also
show that twisted group algebras admit the structure of Frobenius algebras in a
pointed fusion category, and as a consequence, our algebras are Frobenius
algebras in a group-theoretical fusion category. They also enjoy several good
algebraic properties.
