While not luxury, I am happy to find solid mid tier hotels in the Caucasus.
Grand Hyatt Doha
Marriott Yerevan
Hyatt Place Yermuk
Tsaghkadzor Marriott
Radisson Blu Tbilisi
Rooms Hotel Kazbegi, Stepantsminda, a Member of Design Hotels
Rooms Hotel Tbilisi, a Member of Design Hotels
Caresse Bodrum
Park Hyatt Istanbul