Surely the reason Arsenal allowed Giroud to go to Chelsea was the domino effect? By letting him go there Chelsea then let Batshuayi go to Dortmund who in turn let Aubameyang go to Arsenal. I doubt they'd want him to go to Chelsea otherwise.
As for Sanchez, well he was out of contract in the summer and they got Mkhitaryan in return. What you've got to remember is that him and Aubameyang played together at Dortmund (successfully apparently) and they obviously feel they can do well together again at Arsenal.
Us........we got a bloke from The championship who I've never heard off........and Arsenal fans have the temerity to moan! Oh and we are not allowed to sign African players either.
