In theories with Lagrangians that are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations.
These theories appear to have extra degrees of freedom with respect to general relativity; the usual teleparallel Lagrangian, dynamically equivalent to GR, is an exception.
Both facts were overlooked in the f(T) literature but are crucial for assessing f(T) gravity as an explanation of the accelerated expansion of the Universe.