Here's a workaround that's worked very well for me, which is based on the fact that the gmail app can handle outlook invites:
1. Create a rule that sends a copy of all invitation requests to your gmail account
2. Generate a link to your gmail calendar to be used for sharing
3. Use that link to add a calendar to your iCloud account, which will sync with your gmail calendar
4. Open your calendar invite from the gmail app. When you accept the invite it will notify the sender, the event will be added to your gmail calendar and then automatically be added to your IOS calendar.
Once setup properly it works very smoothly. Hope that helps.