The notion of an automorphic form/representation (and sometimes, of Langlands program in tandem) has been extended in many directions - from arithmetic to geometric to topological - but two versions I have not yet come across are for (1)reductive group schemes over more general bases than global fields (whose theory one can find in a paper of Brian Conrad's), and (2)pro-reductive groups (which arise as motivic Galois groups of Andrè's pure motives, for example.)
Does the notion already exist in these settings, or is it waiting its turn to be developed, or are there problems with its generalization in these directions whether technical or motivational?