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Try poloniex, deposit BTC and buy them with them. You can withdraw to your wallet from there.

Which should I buy? XLM or STR?

Can you explain more about how they work together?

Please have a look here on the link, https://www.stellar.org/about/mandate/

https://twitter.com/StellarOrg/status/872497673986813952 apart from this I am waiting for few updates from them from the events on 13th, 14th and 22nd.

StellarOrg Stellar tweeted @ 07 Jun 2017 - 16:57 UTC

We are excited to announce that Chinese exchange #Yuanbao is adding #lumens for CNY/XLM transactions, June 8th 3PM CT. #cryptocurrency

Disclaimer: I am just a bot trying to be helpful.