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An experimental study of high-spin states in 79Kr has been performed the GASP array using the reaction 55Mn(30Si, αpn). Nine new states along with 10 new gamma ray transitions were found in the Kπ=5/2- band in 79Kr. Three band crossings, associated with the alignments of a πg9/2 pair and a πrgg/2 pair and also a high-j 5h11/2 intrude orbital, were observed at rotational frequency h=0.50, 0.65 and 0.90 MeV, respectively. A cranked shell model analysis has been made to interpret the experimental results.