Who is responsible for Jesus' death?
Pilate states in chapter 168 13,14 that he wanted nothing to do with Jesus' death.
13 This man whom you accuse is son of the most holy Gods, and I proclaim my innocence.
14 If you would shed his blood, his blood is on your hands and not on mine.
15 And then the Jews exclaimed, And let his blood be on our hands and on our children's hands.
16 And Pilate trembled like a leaf, in fear. Barabbas he released and as the Lord stood forth before the mob the ruler said, Behold your king! And would you put to death your king?
17 The Jews replied, He is no king; we have no king but great Tiberius.
18 Now, Pilate would not give consent that Roman soldiers should imbue their hands in blood of innocence, and so the chief priests and the Pharisees took counsel what to do with Jesus, who was called the Christ.
19 Caiaphas said, We cannot crucify this man; he must be stoned to death and nothing more.
20 And then the rabble said, Make haste! let him be stoned. And then they led him forth toward the hill beyond the city's gates, where criminals were put to death.
21 The rabble could not wait until they reached the place of skulls. As soon as they had passed the city's gate, they rushed upon him, smote him with their hands, they spit upon him, stoned and he fell upon the ground.
22 And one, a man of God, stood forth and said, Isaiah said, He shall be bruised for our transgressions and by his stripes we shall be healed.
23 As Jesus lay all bruised and mangled on the ground a Pharisee called out, Stay, stay you men! behold, the guards of Herod come and they will crucify this man.
24 And there beside the city's gate they found Barabbas's cross; and then the frenzied mob cried out, Let him be crucified.
25 Caiaphas and the other ruling Jews came forth and gave consent.
The guards of Herod were not under Pilate's command. They were under Herod. Herod had hired Roman soldiers as his guard. But Herod was Jewish not roman. Pilate had no responsibility for Herod's soldiers. Therefore it was the Jews that had crucified Jesus.