Discretionary Access Control (DAC) systems provide powerful mechanisms for resource management based on the selective distribution of capabilities to selected classes of principals. We study a type-based theory of DAC models for concurrent and distributed systems represented as terms of Cardelli, Ghelli and Gordon's pi calculus with groups \cite{CarGheGor:pigroups}. In our theory, groups play the r\^ole of principals, and the structure of types allows fine-grained mechanisms to be specified to govern the transmission of names, to bound the (iterated) re-transmission of capabilities, to predicate their use on the inability to pass them to third parties, $\dots$ and more. The type system relies on subtyping to help achieve a selective distribution of capabilities, based on the groups in control of the communication channels. Type preservation provides the basis for a safety theorem stating that in well-typed processes all names flow according to the delivery policies specified by their types, and are received at the intended sites with the intended capabilities.