The sorting index on colored permutations and even-signed permutations

We define a new statistic sor on the set of colored permutations G_r,n and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of n non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: (ℓ,Rmil⁰,Rmil¹,...,Rmil^r-1, Lmil⁰,Lmil¹,...,Lmil^r-1, Lmal⁰,Lmal¹,...,Lmal^r-1, Lmap⁰,Lmap¹,...,Lmap^r-1) and (sor,Cyc⁰,Cyc^r-1,...,Cyc¹, Lmic⁰,Lmic^r-1,...,Lmic¹, Lmal⁰,Lmal¹,...,Lmal^r-1, Lmap⁰,Lmap¹,...,Lmap^r-1). Analogous results are also obtained for Coxeter group of type D. Our work generalizes recent results of Petersen, Chen-Gong-Guo and Poznanović.