Who invited Imam Husain(a.s) to Kufa?

Who invited, well people of Kufa invited. People of Kufa includes majority sunnis, minority shia of Imam Ali a.s and plus those who saw the majority looking upon Imam Hussain a.s for help and for their worldly gains decided to follow the direction of flowing river.
Again, a sunni brother asked : why would sunni invite as they do not believe in Imamat?

Reason: because for sunnis Imam Hussain a.s was the only living grandson of Prophet s.a.w, the most pious and the leader of youth of paradise. They found him the best option to rule as compare to Yazid. Main stream sunnis were not only in Hijaz but in Kufa also the maority was of those main stream sunnis. Imam Hussain a.s did travel to Makkah first but he saw the place is not free from his killers and so as medina which was under yazid's governor. People of Kufa were willing to fight for justice as it was near Umayyad capital as compare to Hijaz and they were the one getting affected first. 

Abdullah Ibn Zubair also left medina and went into hiding in Makkah, Abdullah Ibn Umar accepted Yazid's rule and Abdur Rehman also went into hidings and it was only Imam Hussain a.s who rose his voice against tyranny. Therefore main stream sunni muslims chose Imam Hussain a.s along with Shias of Imam Ali a.s for help.

 Caliph Umar founded this city and made his people to live in it. Umar ruled for 10-12 years followed by Uthman (Bani Umayyan) for another long period. Ruler of Kufa was cousin of Uthman (foster brother may be) and then comes Imam Ali a.s who ruled for just 5 yrs and then again 6 months of Imam Hassan a.s followed by 20 years of Muawiyah.

Imam Ali a.s did not make Kufa his capital as Shias were in majority. Imam Ali a.s is not only shia leader. It is shias first Imam and sunnis 4th Righteous Guided Caliph so he made that city capital because it was close to western borders where people were making more fitna.

Conclusion: Its nothing about sunni or shia - people are gonna go round thinking their fellow muslims are responsible for the massacre - it was SO long ago and we can't compare the killers to anyone living today. I went to a sunni mosque where they were mourning and remembering ashura.
We are all here to learn from each others.

Initially, Sunnis did not kill imam hussain .. Yazid Army did , and all muslim were against it.
Who is Yazid compare to Imam Hussain . Imam Hussain is a Sayed and also Sayed shabab aljannah.
Imam Hussain was the first person in this world who looked like our prophet