We introduce the concept of group state transfer on graphs, summarize its relationship to other concepts in theory quantum walks, set up a basic theory, and discuss examples. Let X be graph with adjacency matrix A consider walks vertex V(X) governed by continuous time-dependent unitary transition operator U(t)=exp(itA). For S,T⊆V(X), we say admits “group transfer” from S T at time τ if submatri...