Could you show your code? Because i tried to display a pdf in stageWebView and it doesnt work . However, it works when the url is a website.
I have replied to this elsewhere as well, but I think this is an Android problem. I cannot open a PDF in the Android browser, even when just browsing web pages, if I click on a PDF, it downloads and then I have to open it in a PDF capable app like QuickOffice or Adobe Reader. I haven't found any 'plug in' that will enable the Android browser to display a PDF directly.
I think that my problem was i couldnt see pdf in my app running in ipad simulator of FlashBuilder in a flex mobile project in my laptop. what i read said that StageWebView create an instance of default browser in your machine. So that if we cant see pdf in ipad simulator is because also you cant see it in the default browser.
Apart of this, i run this example in other machine, and i could see it, so its not problem of your code, but from your browser probably doesnt have pdf plugin installed. Correct me if i´m wrong.