In the usual setup, consider the category of Harish-Chandra $(\mathfrak{g},K)$-modules with given central character (if the central character is regular, this is equivalent to $K$-equivariant $D$-modules on the flag variety). Assume that everything is split.

I was said that the principal series modules in this category, all are equal in the Grothendieck group (and generically irreducible, so just isomorphic).

I would like a reference for this fact, but which is algebraic; I don't want it to use intertwining operators - one can make the problem meaningful over an algebraically closed field of characteristic $0$, and I want a proof that in principle will work in this purely algebraic context.

Thank you