Hi,
Currently I am not aware of anything that would achieve this besides maybe Using REST services:
https://help.k2.com/onlinehelp/k2blackpearl/UserGuide/4.7/default.htm#ServiceBrokers/EndPoints/REST_Endpoint.htm%3FTocPath%3DAdminister%7CK2%2520Management%2520Site%7CIntegration%7CService%2520Types%7CGeneric%252FEndPoints%2520Service%2520Types%7CREST%7C_____0 However I do believe using, Google Calendar API will help you achieve this:
https://developers.google.com/calendar/overviewMaybe someone else can provide more insight regarding this.
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We do have integrated exchange appointment smartobject which, with a little set up, should do everything needed.