The induced representation of C*-groupoid dynamic systems

Let G be a second countable locally compact groupoid with Haar system {gamma(u)}, H be a closed subgroupoid containing G(0) with Haar system {gamma(H)(u)}. T.Masuda introduced the C*- Groupoid dynamic system (G, A, alpha) and its reduced crossed product C-red(G, A) in [2], where A is a C*-algebra, alpha is the homomorphism G --> Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, alpha\(H)) and (H\G(2), A, <(alpha)over bar>) induced by (G, A, alpha) and proves that C*(red)(H,A) and C*(red)(H\G(2),A) are strongly Morita equivalent. Moreover the induced representation from C*(red)(H, A) to C*(red)(G, A) is got.