Title: Equivariant cellular homology and its applications Author: Boris Chorny AMS Classification numbers Primary 55N91; Secondary 55P91, 57S99 Address of Author Einstein Institute of Mathematics, Edmond Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Email address of Author chorny@math.huji.ac.il Text of Abstract In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.