How can I delete Hotmail emails when using the Gmail app on my phone

I use the Gmail app to read emails on my Android phone. I defined two accounts, a Gmail account and a Hotmail account. The Gmail account works w/o a problem, for syncing, reading, writing and deleting emails. However, when using the Hotmail account, reading and writing emails work fine, but whenever I delete an email (with any of the various standard methods), the email is removed from Inbox, only to re-appear next time the account syncs (of course, when doing this from the web interface, it works just fine). I tried a few solutions, including changing the Outlook options and changing settings on my phone, but nothing seems to work. How can I make my deleted Hotmail emails really disappear?