Ramified Satake Isomorphisms for strongly parabolic characters
  For certain characters of the compact torus of a reductive $p$-adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche. 
Masoud Kamgarpour and Travis Schedler
math.RT