Following an idea and a description of T. Petrie, many authors have constructed exotic smooth group actions using equivariant surgery. This involves the construction of suitable \(G\)-normal maps via \(G\)- transversality, and an arrangement that makes \(G\)-surgery obstructions vanish. It is difficult to find detailed and uptodate statements and proofs concerning the construction of \(G\)-normal maps in the literature. This paper is devoted to those details and their proofs (e.g., for Petrie's transversality theorem) involving steps of both a combinatorial (Burnside ring) and a topological nature. Moreover, it contains nice results about localization in Burnside rings that are essential for the results about smooth one-fixed-point actions of Oliver groups on spheres due to the author, E. Laitinen and K. Pawałowski.