The capital of Ukraine is the City of Kyiv - Article 20 of  Ukrainian Constitution 

Article 20 - The capital of Ukraine is the City of Kyiv - http://www.rada.gov.ua/const/conengl.htm#r1

Yes, google finds more for Kiev than Kyiv, but you shouldn't ignore changes. When you come to KBP you see Kyiv written in yellow colour on the terminal B. Still ignoring? Should we change ukrainian constitution only due to google search result? Definetly, no!!! Of course in USSR Kyiv in every foreign press was spelled as Kiev. As a result it caused a habit to spell name of the capital of Ukraine in wrong way even up to day, but we are not living in USSR anymore. We are living in independent Ukraine and the capital of this country is Kyiv.