This is a report on work in progress with Matthew Greenberg. Let F be a totally real field and let p be a rational prime that for simplicity we assume is inert in F. Let f be a modular form for a totally indefinite quaternion algebra A over F whose local representation at p is Steinberg. We define a Darmon -invariant attached to f, which is a vector of p-adic numbers indexed by the embeddings of F into Cp. This -invariant is defined using the cohomology of a p-arithmetic subgroup of A∗ and is modeled after Darmon's definition of the L-invariant in the case

F=Q,A=M2(Q).

Next we consider certain p-adic Banach space representations of GL2(Fp) denoted B(k,), where k is the vector of weights of f and  is a vector as before. These Banach space representations generalize the construction of Breuil in the case F=Q, and build on work of Schraen. Our main result is that there exist GL2(Fp)-interwining operators from B(k,) to the f-isotypic component of the completed cohomology of A if and only if the vector  is the negative of the Darmon -invariant. This generalizes a result of Breuil in the case F=Q,A=M2(Q).