We show that if X is a cocompact G-CW-complex such that each isotropy
subgroup Gσ is L(2)-good over an arbitrary commutative ring k, then X satisfies some fixed-point
formula which is an L(2)-analogue of Brown’s formula in 1982. Using this result we present a fixed
point formula for a cocompact proper G-CW-complex which relates the equivariant L(2)-Euler
characteristic of a fixed point CW-complex Xs and the Euler characteristic of X/G. As corollaries,
we prove Atiyah’s theorem in 1976, Akita’s formula in 1999 and a result of Chatterji-Mislin in
2009. We also show that if X is a free G-CW-complex such that C∗(X) is chain homotopy
equivalent to a chain complex of finitely generated projective Zπ1(X)-modules of finite length and
X satisfies some fixed-point formula over Q or C which is an L(2)-analogue of Brown’s formula, then
χ(X/G)=χ(2)(X). As an application, we prove that the weak Bass conjecture holds for any finitely
presented group G satisfying the following condition: for any finitely dominated CW-complex Y
with π1(Y )=G, Y satisfies some fixed-point formula over Q or C which is an L(2)-analogue of
Brown’s formula.